Systems, methods, and devices for generating predominantly radially expanded plasma flow

ABSTRACT

Systems, devices, and methods generating a plasma flow are disclosed. A method may include applying energy that alternates between being at a base level for a first duration and at a pulse level for a second duration according to a controlled pattern, generating a plasma flow having a directional axis, and discharging the plasma flow alternating between a base configuration and a pulse configuration according to the controlled pattern. The plasma flow in the base configuration may have (1) a first temperature at the outlet and (2) a first flow front that advances along the directional axis. The plasma flow in the pulse configuration may have (1) a second temperature at the outlet that is greater than the first temperature and (2) a second flow front that advances along the directional axis at a speed greater than the first flow front.

CROSS-REFERENCE TO RELATED APPLICATIONS

The application claims priority to U.S. Provisional Application Ser. No.63/071,787, filed Aug. 28, 2020, the content of which is herebyincorporated by reference in its entirety.

TECHNICAL FIELD

Devices, systems, and methods herein relate to generation of plasmaflow, and specifically to the generation of radially expanded plasmaflows and to practical applications of radially expanded plasma flows.

BACKGROUND

Plasma generating devices play an important role in many areas. Plasmais a phase of matter in which a non-negligible number of particles areionized. Plasma can be generated from a fluid, which is typically a gasat room temperature, referred to as plasma-generating gas. Plasma may begenerated by means of applying energy to the plasma-generating gasflowing through a plasma-generating device. The application of energyresults in a substantial temperature increase of the plasma-generatinggas, which in turn, results in ionization of the plasma-generating gasparticles.

Plasma flows with different characteristics may have applications inindustrial, cosmetic, spraying, medical, and other fields. Plasma flowmay be generated with predetermined properties (e.g., continuous,intermittent) based on the particular application of the plasma flow.Application of energy that is substantially constant, such as a constantdirect current (DC), can result in the generation of a continuous plasmaflow, with properties that do not substantially change over time inoperation. These properties include the shape of the flow, thetemperature distribution, and the static and dynamic pressure of theflow. It has been observed, however, that, while such continuous flowsmay be optimal for some applications, they are not well suited for manyother applications.

Various systems and methods for changing the properties of a plasma flowin operation have been proposed. For example, U.S. Pat. No. 7,589,473discloses systems and methods for generating pulsed plasma or anintermittent plasma flow in which the flow of plasma periodically ceasesduring operation. U.S. Pat. No. 9,089,319 discloses systems and methodsfor the generation of volumetrically oscillating plasma flows. U.S. Pat.No. 9,089,319 further discloses various uses and benefits ofvolumetrically oscillating plasma flows in medical and non-medicalfields. Volumetrically oscillating plasma flows, however, may not beoptimal for some medical applications. For example, due to the changesin the volumetrically oscillating plasma flow's active zone, the effecton the treated surface can be unpredictable. Moreover, changes in thedevice's position with respect to the treated surface can produceuncertain and often undesirable results. Additionally, certainconditions for generating volumetrically oscillating plasma flows arenot optimal for certain applications, including medical applications,and can introduce unnecessary requirements on a plasma-generatingdevice.

Existing and previously used power supply systems, as well as plasmagenerating devices, may not be adequate to meet the requirements forgeneration of useful and stable plasma flows. For example, existingpower supply systems may not be capable of generating energy patternsnecessary for generations of certain plasma flows. Generation of certainplasma flows can also cause the rapid destruction of internalcomponents, rendering existing devices unsuitable for real-lifeapplications, especially in the medical field.

Accordingly, there exists a need for systems and methods that generateplasma flows that exhibit substantially uniform, or homogeneous,characteristics over a substantial distance range from the outlet of thedevice.

SUMMARY

Described herein are devices, systems, and methods for generating apredominantly radially expanded plasma flow. These devices and systemsmay generate plasma flows that exhibit substantially uniform, orhomogeneous, characteristics over a predetermined distance.

In some embodiments, a method may comprise supplying a plasma-generatinggas to a plasma generating device having an outlet, applying energy tothe plasma-generating gas according to a predetermined energy pattern,and discharging, in response to applying the energy, a plasma flow fromthe outlet of the plasma generating device, the plasma flow having aperiodic pattern including a base plasma flow and a pulse plasma flow.The base plasma flow having a first temperature at the outlet of thedevice, and the pulse plasma flow having a second temperature at theoutlet of the device that is greater than the first temperature. Thebase plasma having a first density at the first temperature, and thepulse plasma having a second density at the second temperature, thefirst density being at least two times the second density. The baseplasma flow having a first speed of sound, and the pulse plasma flowhaving a second speed of sound that is at most about four times greaterthan the first speed of sound.

In some embodiments, the pattern may include alternating betweendischarging the base plasma flow for a base duration and discharging thepulse plasma flow for a pulse duration, the pulse duration being lessthan the base duration.

In some embodiments, the plasma-generating gas may be supplied at apredetermined flow rate, and the sum of the base duration and the pulseduration may be based at least in part on the flow rate. In someembodiments, the sum of the base duration and the pulse duration may befurther based on the second temperature. In some embodiments, the secondtemperature may be less than or equal to 15,000 K, a ratio of thepredetermined flow rate G (L/min) of the plasma-generating gas to adiameter d (mm) of the outlet may be less than or equal to 100, and thesum of the base duration and the pulse duration may be less than

$100,000*{\frac{d^{4}}{G^{2}}.}$

In some embodiments, the second temperature may be less than or equal to15,000 K, a ratio of the predetermined flow rate G (L/min) of theplasma-generating gas to a diameter d (mm) of the outlet may be greaterthan 100, and the sum of the base duration and the pulse duration may beless than 5 ms. In some embodiments, the second temperature may begreater than 15,000 K, a ratio of the predetermined flow rate G (L/min)of the plasma-generating gas to a diameter d (mm) of the outlet may beless than or equal to 100, and the sum of the base duration and thepulse duration may be less than

$5,{000*{\frac{d^{4}}{G^{2}}.}}$

In some embodiments, the second temperature may be greater than 15,000K, a ratio of the predetermined flow rate G (L/min) of theplasma-generating gas to a diameter d (mm) of the outlet may be greaterthan 100, and the sum of the base duration and the pulse duration may beless than 500 μs. In some embodiments, a frequency of the alternatingbetween the base plasma flow and the pulse plasma flow may be greaterthan about 1 kHz. In some embodiments, a diameter of the outlet may beless than about 140 mm when the second temperature is less than or equalto about 10,000 K. In some embodiments, the plasma-generating gas may besupplied at a predetermined flow rate that is directly proportional to adiameter of the outlet.

In some embodiments, if the diameter of the outlet is about 0.5 mm, thepredetermined flow rate may be between about 0.5 l/min and about 4l/min, if the diameter of the outlet is about 5 mm, the predeterminedflow rate may be between about 5 l/min and about 40 l/min, and if thediameter of the outlet is about 10 mm, the predetermined flow rate maybe between about 10 l/min and about 80 l/min.

In some embodiments, the plasma flow may have an outlet temperature-timeprofile that includes a repeated set of regions, the repeated set ofregions including a first region in which the plasma flow has an outlettemperature maintained at the first temperature, a second region inwhich the outlet temperature of the plasma flow rises to the secondtemperature, a third region in which the outlet temperature of theplasma flow reduces at a first rate to a third temperature, a fourthregion in which the outlet temperature of the plasma flow reduces at asecond rate to a fourth temperature, and a fifth region in which theoutlet temperature of the plasma flow reduces at a third rate to thefirst temperature. In some embodiments, the second rate may be greaterthan the first and third rates. In some embodiments, the outlettemperature may rise to the second temperature in the second regionduring a time interval of about 0.01 to about 0.1 times the totalduration of the set of regions. In some embodiments, the outlettemperature may reduce to the fourth temperature in the fourth regionduring a time interval of about 0.01 to about 0.1 times the totalduration of the set of regions. In some embodiments, the outlettemperature may reduce to the first temperature in the fifth regionduring a time interval of about 0.2 to about 0.4 times the totalduration of the set of regions. In some embodiments, the fourthtemperature may be an intermediate temperature between the first andthird temperatures, the fourth temperature being equal to about 0.2 toabout 0.4 times a difference between the first and third temperatures.In some embodiments, the total duration of the set of regions may bebetween about 10 and about 50 μs. In some embodiments, the firsttemperature may be between about 2,000 K and about 4,000 K.

In some embodiments, a system may comprise a current control generatorconfigured to supply current having a current pattern to aplasma-generating device such that the plasma-generating device cangenerate a radially expanded plasma flow, the current pattern including:a first set of oscillations between a first base level and a second baselevel, the second base level being greater than the first base level,the first set of oscillations having a first frequency, and a second setof oscillations between a first pulse level and a second pulse level.The second pulse level being greater than the first pulse level and thefirst and second base levels. The second set of oscillations having asecond frequency greater than the first frequency. The first and secondsets of oscillations being synchronized such that the first base levelis paired with the first pulse level for generating the radiallyexpanded plasma flow and the second base level is paired with the secondpulse level for generating the radially expanded plasma flow.

In some embodiments, the first set of oscillations may have a currentpulse resolution between about 0.1 ms to about 0.2 ms. In someembodiments, the second set of oscillations may have a current pulseresolution between about 0.1 μs and 1μs. In some embodiments, a rootmean square of the current having the current pattern is between about12 A and about 15 A.

In some embodiments, the second set of oscillations may include arepeated set of regions, the repeated set of regions including: a firstregion in which the current maintained at the first base level or thesecond base level, a second region in which the current rises to a firsttop pulse level from the first base level or a second top pulse levelfrom the second base level, a third region in which the current reducesto a first bottom pulse level from the first top pulse level or a secondbottom pulse level from the second top pulse level, a fourth region inwhich the current reduces to a first intermediate level from the firstbottom pulse level or a second intermediate level from the second bottompulse level, and a fifth region in which the current reduces to thefirst base level from the first intermediate level or the second baselevel from the second intermediate level.

In some embodiments, the current may reduce to the first bottom pulselevel or the second bottom pulse level at a first rate, and the currentmay reduce to the first intermediate level or the second intermediatelevel at a second rate, the second rate being greater than the firstrate.

In some embodiments, the current may reduce to the first bottom pulselevel or the second bottom pulse level at a first rate, the current mayreduce to the first intermediate level or the second intermediate levelat a second rate, and the current may reduce to the first base level orthe second base level at a third rate, the second rate being greaterthan the first and third rates.

In some embodiments, the current may rise to the first top pulse levelor the second top pulse level in the second region during a timeinterval of about 0.01 to about 0.1 times the total duration of the setof regions. In some embodiments, the current may reduce to the firstintermediate level or the second intermediate level in the fourth regionduring a time interval of about 0.01 to about 0.1 times the totalduration of the set of regions.

In some embodiments, the current may reduce to the first base level orthe second base level in the fifth region during a time interval ofabout 0.2 to about 0.4 times the total duration of the set of regions.In some embodiments, the first intermediate level may be about 0.2 toabout 0.4 times a difference between the first bottom pulse level andthe first base level, and the second intermediate level may be about 0.2to about 0.4 times a difference between the second bottom pulse leveland the second base level. In some embodiments, the first frequency ofthe first set of oscillations may be between about 100 Hz and about 2000Hz.

In some embodiments, a plasma-generating device may be configured toheat, in response to receiving the current, a plasma-generating gas, anddischarge, in response to heating the plasma-generating gas, theradially expanded plasma flow alternating between a low intensity plasmaflow and a high intensity plasma flow from an outlet. The low intensityplasma flow being associated with the first base level and the highintensity plasma flow being associated with the second base level.

In some embodiments, the plasma-generating device may be configured todischarge the low intensity plasma flow to heat a treated specimen. Insome embodiments, the plasma-generating device may be configured todischarge the high intensity plasma flow to vaporize or sublimate atreated specimen. In some embodiments, the low intensity plasma flow hasa first degree of radial expansion, and the high intensity plasma flowhas a second degree of radial expansion that is different than the firstdegree of radial expansion. In some embodiments, the first degree ofradial expansion may be greater than the second degree of radialexpansion. In some embodiments, the plasma flow may include an activezone defined by plasma having a temperature above 1,000 K, the activezone having a diameter that is at least ten times greater than adiameter of the outlet.

In some embodiments, a plasma-generating device may comprise a cathodeincluding a tapered distal portion, an anode disposed downstream fromthe cathode and being electrically insulated from the cathode, the anodedefining an opening therethrough. A plurality of intermediate electrodesmay be disposed between the cathode and the anode, the plurality ofintermediate electrodes electrically insulated from each other and fromthe anode and the cathode, each intermediate electrode from theplurality of intermediate electrodes defining an opening therethroughsuch that the openings in the plurality of intermediate electrodes andthe anode collectively define a plasma channel for discharging a plasmaflow, the plasma channel including: a first portion having a firstcross-sectional diameter; and a second portion having a secondcross-sectional diameter, the first cross-sectional diameter being atleast four times the second cross-sectional diameter; an insulatorsleeve extending along a surrounding a portion of the cathode.

In some embodiments, a distance from a distal end of the cathode to thesecond portion of the plasma channel may be at least 1.25 times thesecond cross-sectional diameter. In some embodiments, a ratio of alength of a portion of the cathode protruding beyond a distal edge ofthe insulator sleeve to a maximum diameter of the catheter being betweenabout 1.0 and about 1.6. In some embodiments, a ratio of a length of thetapered distal portion of the cathode to a maximum diameter of thecathode may be between about 1.5 and about 2.0. In some embodiments, thesecond cross-sectional diameter may have between about 0.4 mm and about1.0 mm. In some embodiments, the anode may form an anode portion of theplasma channel, and a ratio of a length of the anode portion to adiameter of the anode portion may have between about 2 and about 4.

In some embodiments, the anode portion may have an outlet diameter ofbetween about 0.3 mm and about 0.6 mm. In some embodiments, the openingin the anode may have a cross-sectional diameter at a proximal end ofthe anode that is less than a cross-sectional diameter at a distal endof the anode. In some embodiments, an outer sleeve may be coupled to theanode; and a divider disposed between the outer sleeve and the pluralityof intermediate electrodes, the divider with outside surfaces of theplurality of intermediate electrode, an outside surface of the anode,and an inside surface of the outer sleeve collectively defining acooling channel for cooling the plasma channel. In some embodiments, thecathode may be disposed in a cathode chamber having a diameter dcc, thediameter dcc being at least four times the second cross-sectionaldiameter. In some embodiments, a length of the anode may be betweenabout two times to about eight times a diameter of the anode. In someembodiments, the anode may have a shape of an adaptive nozzle.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a plasma-generating device, accordingto an embodiment.

FIG. 2 is a plot of plasma flow temperature and time, according to anembodiment.

FIG. 3 is a schematic diagram of generated plasma, according to anembodiment.

FIGS. 4A-4F are schematic diagrams of continuous plasma andpredominantly radially expanded plasma, according to an embodiment.

FIG. 5 is a plot of plasma flow temperature and time, according to anembodiment.

FIGS. 6A-6K are schematic diagrams of plasma flow volumes correspondingto the temperature and time plot of FIG. 5 , according to an embodiment.

FIG. 7 is a plot of plasma flow temperature and time, according to anembodiment.

FIGS. 8A-8E are schematic diagrams of plasma flow corresponding to thetemperature and time plot of FIG. 7 , according to an embodiment.

FIG. 9 is a plot of temperature and time of a rectangular pulse,according to an embodiment.

FIG. 10 is a plot of inlet pressure and argon mass flux dependence forsteady laminar flow, according to an embodiment.

FIG. 11 is a plot of gas flow and inlet pressure dependence onoscillating outlet temperature, according to an embodiment.

FIGS. 12A-12C are schematic diagrams of choking conditions forillustrative outlets, according to an embodiment.

FIG. 13 is a plot of measured argon plasma flows with fixed mass flowrates, according to an embodiment.

FIGS. 14A and 14C are plots of plasma flow temperature and time for asingle pulse of constant outlet temperature. FIGS. 14B and 14D are plotsof temperature and distance corresponding to respective FIGS. 14A and14C, according to an embodiment.

FIG. 15A is a plot of temperature and time of a pulsed plasma flow,according to an embodiment. FIGS. 15B and 15C are plots of temperatureand distance of the pulsed plasma flow corresponding to FIG. 15A,according to an embodiment.

FIG. 16 is a plot of plasma temperature and density profiles along aflow axis for steady laminar flow with constant outlet temperature,according to an embodiment.

FIG. 17 is a schematic diagram of plasma flow with oscillating outlettemperature and equal length of target and initiator flows, according toan embodiment.

FIG. 18 is a plot of length and time of interactions of low and hightemperature plasma flow with high frequency pulses, according to anembodiment.

FIG. 19 is a schematic diagram of plasma flow with oscillating outlettemperature, according to an embodiment.

FIG. 20 is a plot of length and time of interactions of low and hightemperature plasma flow with high frequency pulses, according to anembodiment.

FIG. 21 is a schematic diagram of plasma flow with oscillating outlettemperature, according to an embodiment.

FIG. 22 is a plot of length and time of interactions of low and hightemperature plasma flow with high frequency pulses, according to anembodiment.

FIGS. 23A-23C are plots of radial oscillation ratio and length in aninteractive volume of plasma flow, according to an embodiment.

FIG. 24 is a plot of target-initiator velocity ratio and pressure forRayleigh and choked flows, according to an embodiment.

FIG. 25 is a plot of duty and density ratio relationships for radialexpansion with argon as a plasma generating gas, according to anembodiment.

FIG. 26 is a plot of target temperature and initiator temperature foroptimal radial expansion, according to an embodiment.

FIG. 27 is a plot of duty and density ratio relationships for radialexpansion with air as a plasma generating gas, according to anembodiment.

FIG. 28 is a plot of plasma flow pressure and inlet pressure, accordingto an embodiment.

FIG. 29 is a plot of plasma jet length and inlet gas flow, according toan embodiment.

FIG. 30 is a plot of dependence of maximum outlet diameter on inlet gasflow for various outlet temperatures, according to an embodiment.

FIG. 31 is a plot of dependence of maximum period on outlet diameter forvarious outlet pulse temperatures, according to an embodiment.

FIG. 32 is a plot of dependence of maximum period on outlet pulsetemperature, according to an embodiment.

FIG. 33 is a plot of dependence of minimum frequency on outlet pulsetemperature, according to an embodiment.

FIG. 34 is a plot of dependence of maximum outlet diameter on outletpulse temperature, according to an embodiment.

FIG. 35 is a plot corresponding to a critical gas flow rate for aReynolds number of 2000, according to an embodiment.

FIG. 36 is a plot corresponding to frequency relationships for avoidingsignificant heating of low intensity plasma, according to an embodiment.

FIGS. 37A-37C are plots of length and time corresponding to frontpropagation dynamics for target and initiator plasma flows depending onthe frequency of outlet temperature oscillations, according to anembodiment.

FIGS. 37D-37F are plots of temperature and time of outlet temperatureoscillations corresponding to respective FIGS. 37A-37C, according to anembodiment.

FIGS. 38A-38C are plots of length and time corresponding to frontpropagation dynamics for target and initiator plasma flows depending onthe shape of outlet temperature oscillations, according to anembodiment.

FIGS. 38D-38F are plots of temperature and time of outlet temperatureoscillations corresponding to respective FIGS. 38A-38C, according to anembodiment.

FIGS. 39A-39C are schematic diagrams of plasma flow and tissue,according to an embodiment.

FIG. 40 is a plot of amplitude and time for oscillation outlettemperature, according to an embodiment.

FIG. 41 is a plot of inlet gas flow and inlet pressure for boostingworking pressure by oscillation of outlet temperature with two levels ofamplitudes and frequencies, according to an embodiment.

FIGS. 42A-42J are schematic diagrams of plasma jet shapes depending onan input and outlet temperature-time profile, according to anembodiment.

FIG. 43 is a plot of amplitude and time for temperature-time profile andinput parameters, according to an embodiment.

FIG. 44 is a plot of lower and upper boundaries for pulse temperaturefor argon plasma, according to an embodiment.

FIG. 45 is a plot of lower and upper boundaries for pulse temperaturefor argon plasma, according to an embodiment.

FIG. 46 is a plot of lower and upper boundaries for pulse temperaturefor air plasma, according to an embodiment.

FIG. 47 is a plot of dependence of maximum period on outlet basetemperature, according to an embodiment.

FIG. 48 is a plot of dependence of minimum frequency on outlet basetemperature, according to an embodiment.

FIG. 49 is a plot of dependence of maximum outlet diameter on outletbase temperature, according to an embodiment.

FIG. 50 is a plot of dependence of maximum inlet gas flow on basetemperature for pulse-base ratio, according to an embodiment.

FIG. 51 is a plot of dependence of maximum inlet gas flow on pulsetemperature for pulse-base ratio, according to an embodiment.

FIG. 52 is a plot of dependence of minimum inlet gas flow on basetemperature for pulse-base ratio, according to an embodiment.

FIG. 53 is a plot of dependence of minimum inlet gas flow on pulsetemperature for pulse-base ratio, according to an embodiment.

FIG. 54 is a plot of a temperature-time profile, according to anembodiment.

FIG. 55 is a cross-sectional side schematic view of a plasma-generatingdevice, according to an embodiment.

FIG. 56 is a cross-sectional side schematic view the plasma-generatingdevice depicted in FIG. 55 , according to an embodiment.

FIG. 57 is a cross-sectional side schematic view of anotherplasma-generating device, according to an embodiment.

FIG. 58 is a cross-sectional side schematic view of measurement pointsof a plasma-generating device, according to an embodiment.

FIG. 59 is a plot of average temperature distribution along a heatingchannel, according to an embodiment.

FIG. 60 is a plot of average temperature distribution along a heatingchannel for relatively high current, according to an embodiment.

FIG. 61 is a plot of average temperature distribution along a heatingchannel for relatively low current, according to an embodiment.

FIG. 62 is a plot of an average temperature distribution along a heatingchannel for relatively high current, according to an embodiment.

FIGS. 63A-63C are plots of current oscillation for performance tests,according to an embodiment.

FIG. 64 is a plot of lifespan acceptance criteria and cathode chamberdiameter, according to an embodiment.

FIGS. 65A-65B are plots of volt-ampere characteristics for U_(C-E1) andU_(E1-A), according to an embodiment.

FIGS. 66A-66B are plots of a time scan of U_(C-E1) for relatively lowand relatively high frequency, according to an embodiment.

FIGS. 67A-67B are plots of a time scan of U_(C-E1) for a set of pulseintervals, according to an embodiment.

FIG. 68 is a plot of a time scan of U_(C-E1), according to anembodiment.

FIG. 69 is a plot of residual voltage U_(res) and time, according to anembodiment.

FIG. 70 is a plot of peak-to-base voltage U_(p-b) and time, according toan embodiment.

FIG. 71 is a plot of ion concentration in the proximity of a cathodesurface in case of steady-state operation at constant current, accordingto an embodiment.

FIG. 72 is a plot of ion concentration in the proximity of a cathodesurface depending on a ratio d_(cc)/d_(h), according to an embodiment.

FIG. 73 is a plot of a time scan of arc current U_(C-E1) and powerdensity for d_(cc)/d_(h)=2, according to an embodiment.

FIG. 74 is a plot of a time scan of arc current U_(C-E1) and powerdensity for d_(cc)/d_(h)=4, according to an embodiment.

FIG. 75 is a plot of a time scan of arc current and conductivity for anoscillating arc current, according to an embodiment.

FIGS. 76A-76D are cross-sectional side schematic views of a spot anddiffuse mode of arc attachment, according to an embodiment.

FIG. 77 is a plot of current and time for frequency oscillation,according to an embodiment.

FIG. 78 is a plot of ratio estimation of vaporized layer thickness toheat penetration length, according to an embodiment.

FIGS. 79A-79C are plots of current patterns to reduce the effectivevaporization rate, according to an embodiment.

FIG. 80 is a plot of increasing pulse outlet mass flux with higherworking pressure in a plasma-generating device, according to anembodiment.

FIG. 81A is a schematic diagram of plasma flow for current pulses and arelatively low base current level between pulses, according to anembodiment.

FIG. 81B is a plot of current and time corresponding to FIG. 81A,according to an embodiment.

FIG. 82A is a schematic diagram of plasma flow depending on current baselevel and degree of radial expansion, according to an embodiment.

FIG. 82B is a plot of current and time corresponding to FIG. 82A,according to an embodiment.

FIG. 83A is a plot of current and time for vaporization, according to anembodiment.

FIG. 83B is a plot of current and time for controlled heating, accordingto an embodiment.

FIG. 84A is a plot of current and time for vaporization and heating,according to an embodiment.

FIG. 84B is a schematic diagram of plasma flow corresponding to FIG.84A, according to an embodiment.

FIG. 85 is a plot of current drop over time, according to an embodiment.

FIG. 86 is a set of schematic diagrams of different combinations ofrelatively high and relatively low plasma flows, according to anembodiment.

FIG. 87 is a plot of current and time applied within a plasma-generatingdevice, according to an embodiment.

FIG. 88 is a plot of temperature and time of an outlet plasma flow,according to an embodiment.

FIG. 89 is a plot of an example high frequency pulse, according to anembodiment.

DETAILED DESCRIPTION 1. Overview of Radially Expanded Plasma Flows

Plasma flows with different characteristics can be used for variousapplications, such as industrial, cosmetic, spraying, medical, andothers. A plasma flow is a stream of gas particles in which anon-negligible number of gas particles are ionized. Plasma is generatedfrom a fluid, which is typically a gas at room temperature, referred toas plasma-generating gas. Plasma may be generated by means of applyingenergy to the plasma-generating gas flowing through a plasma-generatingdevice. The application of energy results in a substantial temperatureincrease of the plasma-generating gas, which in turn, results inionization of the plasma-generating gas particles. In some embodiments,plasma flow may be generated by heating a stream of plasma-generatinggas to a predetermined temperature to ionize a substantial portion ofthe gas particles.

Various systems and methods can be used to change the properties orcharacteristics of a plasma flow. These properties include the shape ofthe flow, the temperature distribution, and the static and dynamicpressure of the flow. For example, U.S. Pat. No. 7,589,473 disclosessystems and methods for generating pulsed plasma or an intermittentplasma flow in which the flow of plasma periodically ceases duringoperation. As another example, embodiments for generating volumetricallyoscillating plasma flows are described in U.S. Pat. No. 9,089,319, filedJul. 22, 2010, and titled “VOLUMETRICALLY OSCILLATING PLASMA FLOWS,”U.S. Pat. No. 8,613,742, filed Jan. 29, 2010, and titled “METHODS OFSEALING VESSELS USING PLASMA,” the contents of each of which are herebyincorporated by reference in their entirety. Such embodiments can changea shape, temperature distribution, or other properties of a plasma flow.In some applications, however, such embodiments can cause significantdifferences in treatment in response to deviations in device positioningor operating conditions. Additionally, such embodiments can producevolumetrically oscillating plasma flows with low intensity plasma havinga temperature at the device outlet of at least 10,000 K and highintensity plasma having a temperature exceeding the low intensity plasmatemperature by at least 10,000 K. In some applications including medicalapplications, however, such temperatures are not suitable and canintroduce unnecessary requirements on the plasma-generating device.Devices and methods described in U.S. Pat. Nos. 9,089,319 and 8,613,742can also be improved to extend the life of various device components.Systems, devices, and methods described herein can generate plasma flowsthat exhibit substantially uniform or homogenous characteristics over asubstantial distance from an outlet of a plasma-generating devicewithout certain drawbacks.

FIG. 1 is a schematic diagram of a plasma-generating device 100 (e.g.,plasma generating device). A plasma-generating device 100 may include acontroller 102 (e.g., gas flow controller). The controller 102 may beconfigured to supply a gas for plasma generation at a constantpredetermined rate of G_(IN) (e.g., about 0.5 L/min) to expansionchamber 104. The controller 102 may be configured to supply theplasma-generating gas into expansion chamber 104, which is used toreduce the effect of inlet pressure P_(IN) deviations in response tovarying energy that is used to heat plasma-generating gas downstream.From the expansion chamber 104, the plasma-generating gas may flow intoa channel 106 (e.g., active chamber, heating channel). The channel 106may be configured to heat the plasma-generating gas using energyprovided (e.g., applied, supplied) from power source 108. In someembodiments, the heating channel may comprise a diameter d_(H). Energymay be applied to the plasma-generating gas inside the channel 106 toincrease the gas temperature to thereby generate particle ionization. Insome embodiments, the energy may be in the form of one or more ofelectromagnetic energy, electric energy, combinations thereof, and thelike. As a result of this heating, plasma flow 120 may be dischargedfrom outlet 110 of channel 106. In some embodiments, the outlet 110 canhave a diameter dour.

FIG. 2 is a plot of the temperature of plasma flow 120 generated as aresult of heating a plasma-generating gas according to a predeterminedpattern (e.g., controlled pattern, a series of current pulses). As shownin FIG. 1 , the plasma flow 120 can define an axis 130, which representsa center line of the plasma flow extending in the direction of theplasma flow 120. The plasma flow 120 can include an active zone orvolume of active plasma, which includes plasma having a temperatureabove a predetermined threshold. For example, the predeterminedthreshold temperature may be about 1,000 K. In some embodiments, theactive zone may expand and contract volumetrically over time accordingto a controlled pattern such as, for example, a controlled patternassociated with a pattern of current or power density delivered to theplasma-generating device. In some embodiments, the active plasma canoccupy a space as a volume of the plasma. The plasma flow 120 can becharacterized by a length or a distance between an outlet of aplasma-generating device (e.g., outlet 110) and a point along axis 130where the plasma comprises a threshold temperature. Alternatively oradditionally, the plasma flow 120 can be characterized by a width atdifferent points along the axis 130. Width with respect to the plasmaflow in a predetermined plane transverse to the plasma flow axis can bethe diameter of the active plasma in the predetermined plane.Additionally, width can generally refer to a maximum width or maximumlateral dimension of the plasma flow.

In some embodiments, the plasma flow 120 can be characterized bytemperature and, specifically, a temperature at the outlet 110 of theplasma-generating device. Unless specifically stated otherwise, the term“temperature” with respect to a plasma flow refers to the temperature ofthe plasma flow at an outlet of a plasma-generating device or when theplasma first exits a plasma-generating device. For example, a generatedplasma flow having a temperature of about 8,000 K corresponds to aplasma flow having a temperature of about 8,000 K at the outlet of theplasma-generating device 100. In some embodiments, the temperature maynot be uniform along the axis 130 and may decrease as a function ofdistance from the outlet 110 along the axis 130 and as a function ofdistance in a direction transverse to the axis 130. In some embodiments,the plasma flow can be continuous and have properties (e.g., shape ofthe flow, temperature distribution, static and dynamic pressure of theflow) that do not substantially change over time during operation of aplasma-generating device. For example, a constant direct current (DC)(e.g., application of substantially constant energy) may generate acontinuous plasma flow. Additionally or alternatively, the plasma flowcan be intermittent or periodically cease during operation. Whilecontinuous flows can be useful for certain applications, in otherapplications, intermittent flows may be more suitable.

In some embodiments, under a first set of conditions, the plasma flow120 remains laminar. A laminar flow may be characterized by fluidflowing in lamina or layers with substantially no exchange of fluid(e.g., mixing) between the neighboring lamina. Laminar flow may occurwhen viscous forces of a fluid are comparable to inertial forces. Insome embodiments, under a second set of conditions, the plasma flow 120can be a turbulent flow. Turbulent flow may occur when the inertialforces of plasma predominate over the viscous forces. A turbulent flowmay be characterized by a rapid and chaotic variation of pressure andvelocity in space and time. When a plasma flow is turbulent, the plasmaflow may mix with the surrounding air. This mixing process may produce arapid drop in temperature as the plasma flow propagates, thus formingunpredictable turbulent flow. Systems, methods, and devices describedherein can be configured to generate plasma flows that are laminarplasma flows, which can avoid drawbacks associated with turbulent flows.

In some embodiments, systems, devices, and methods disclosed herein cangenerate radially expanded flows by using controlled repeated radialexpansion with a number of predetermined parameters, as describedherein. The radially expanded flows can be laminar plasma flows. Suchrepeated radial expansion of a plasma flow increases the flow's width,which can cause the flow's volume to assume a bottle-like shape. FIG. 3depicts a radially expanded flow, where generated plasma 300 takes on abottle-like shape. In some embodiments, repeated (e.g., periodic,intermittent) application of energy to generate a plasma flow mayincrease the width of a plasma flow hundreds or even thousands of timesper second. Such radial expansion can cause the plasma flow to have avolume that assumes the generally bottle-like shape 300. Such plasmaflows, referred to as predominantly radially expanded plasma flows, canhave a width that becomes substantially larger than a diameter of anoutlet (e.g., outlet 310) of a plasma-generating device. Continuousplasma flows, on the other hand, are unable to generate the bottle-likeshape 300 and have such radial expansion.

For illustrative purposes, and to provide context for understanding thebenefits of predominantly radially expanded plasma flows, the propertiesof such flows can be compared to those of continuous plasma flows, asdepicted in the following figures. FIGS. 4A-4F facilitate comparisonbetween the properties of predominantly radially expanded flows 450 tothose of continuous flows 400. FIG. 4E depicts a continuous plasma flow400 having a corresponding radial temperature distribution 410 depictedin FIG. 4A. For example, the temperature distribution 410 of acontinuous plasma flow 400 may be substantially parabolic. That is, thetemperature of the plasma flow may be the highest at the axis 412 andmay drop rapidly toward the periphery. Also, as shown in FIG. 4C, such acontinuous plasma flow 400 may exhibit a substantial temperature 420decrease as a function of a distance traversed with respect to an outletof a plasma-generating device. FIG. 4F depicts a predominantly radiallyexpanded plasma flow 450 having a corresponding temperature distribution460 depicted in FIG. 4B. The volume of flow 450 depicted in FIG. 4F maybe similar to that depicted in FIG. 3 . For example, the volume ofplasma flow 450 may have a shape resembling a bottle with its neckfacing outlet 452. As depicted in FIGS. 4B and 4D, the radial and axialdistribution of temperature, respectively shown, may vary less within apredetermined volume. In some embodiments, the temperature distributionscan be substantially uniform or constant over a certain distanceradially out from the center axis of the plasma flow or a certaindistance axially out from the outlet of the plasma-generating device.

In some embodiments, a plasma flow having a generally bottle-shapedvolume and associated temperature profiles can provide an increasedmargin for error for an operator performing a treatment procedure usingsuch a plasma flow, thus potentially reducing adverse effects of plasmatreatment due to human error and inexperience. For example, continuousplasma flows, including some volumetrically oscillating plasma flows,can require an operator to hold a plasma-generating device at apredetermined distance from and at a predetermined angle relative to atreatment surface. Deviations from a predetermined position of theplasma-generating device with respect to the surface being treated mayresult in detrimental and often irreversible damage to a patient. Bycontrast, predominantly radially expanded plasma flows may provide moreuniform (e.g., substantially uniform) plasma properties in the activezone to increase the predetermined distances and angles relative to thetreatment surface used by an operator.

In some embodiments, the volume of a plasma flow may comprise apredetermined shape based on relatively rapid changes in the energyapplied to the plasma-generating gas. For example, for aplasma-generating device (e.g., plasma-generating device 100) configuredto apply energy to a plasma-generating gas passing through it, asubstantial portion of the plasma-generating gas particles may beionized by the applied energy and converted to plasma discharged from anoutlet of the plasma-generating device.

Radially oscillating plasma flows may be the result of collisions of acombination of relatively fast moving particles of a high intensity,high temperature, and low density plasma flow with relatively slowmoving particles of a low intensity, low temperature, and high densityplasma flow. As used herein, high and low, and fast and slow arerelative terms used to characterize the different plasma flows relativeto one another. For example, an 8,000 K plasma flow may be highintensity compared to a 3,000 K plasma flow and low intensity comparedto a 15,000 K plasma flow. As used herein, low intensity plasma flow canalso be referred to as a base plasma flow and high intensity flow canalso be referred to as a pulse plasma flow. Base plasma flow maygenerally be generated using the base energy, and pulse plasma flow maygenerally be generated using a pulse of energy.

FIGS. 5-8E illustrate the interactions between base plasma flow andpulse plasma flow, and how timing of pulsing can impact the resultingshape of the plasma flow. FIGS. 5 and 6A-6K depict generation of anembodiment of plasma flow where the base plasma flow and the pulseplasma flow are fully allowed to develop. FIG. 5 is a plot oftemperature and time where a base plasma temperature has beenestablished at an outlet of the plasma-generating device at time t₀. Attime t₁, the plasma temperature at an outlet of the plasma-generatingdevice is increased to a pulse plasma temperature and maintained untiltime t₉, at which point the temperature is decreased back to the baseplasma temperature and is maintained at that temperature through timet₁₀.

As depicted in FIGS. 5 and 6A-6K, the base plasma flow and the pulseplasma flow may both have an effect on a treated surface with the pulseplasma flow having a substantially greater effect. FIGS. 6A-6K areschematic diagrams of volumes of plasma flow corresponding to thetemperature and time plot of FIG. 5 . As shown, the radial expansiondepicted in FIGS. 6B-6H may be temporary and unstable. FIG. 6A depicts ashape (e.g., volume) of plasma flow corresponding to time to whereplasma is heated to a base temperature at the outlet. FIG. 6B depicts ashape of the plasma flow corresponding to time ti where pulse plasmaflow is generated at the outlet and where relatively fast movingparticles begin to collide with the relatively slow moving particles ofthe base plasma flow in front of them. FIG. 6C depicts a shape of theplasma flow corresponding to time t₂ where the relatively fast movingparticles of the pulse plasma flow propagate further (relative to FIG.6B) to generate the radial expansion over about half the length of thebase plasma flow. FIG. 6D depicts a shape of the plasma flowcorresponding to time t₃ where the relatively fast moving particles ofthe pulse plasma flow propagate even further (relative to FIGS. 6B and6C) to cover radial expansion over the entire length of the base plasmaflow.

As depicted in FIGS. 6A-6K, the radial expansion of the plasma flow maybe greatest at a distance almost equal to the length of the base plasmaflow. This is because the ratio of densities of the base plasma flow topulse plasma flow may be largest at the distal end of the plasma flow.At the distance equal to the length of the base plasma flow, the baseplasma flow may have cooled off and become denser while the pulse plasmaflow may not have significantly cooled off. FIG. 6E depicts a shape ofthe plasma flow corresponding to time t₄ where the radially expandedplasma flow exists but the pulse plasma flow has overshot the length ofthe base plasma flow and extends further from the outlet than the baseplasma flow. This process continues in FIG. 6F that depicts a shape ofthe plasma flow corresponding to time t₅ where the pulse plasma flowreaches its maximum length while the radially expanded flow stillexists. FIG. 6G depicts a shape of the plasma flow corresponding to timet₆ where the pulse plasma flow is maintained but the radially expandedplume shape begins to dissipate starting from the locations closest tothe outlet. FIG. 6H depicts a shape of the plasma flow corresponding totime t₇ where the radially expanded plume shape is near the locationcorresponding to the length of the base plasma flow. FIG. 61 depicts ashape of the plasma flow corresponding to time t₈ where the radiallyexpanded plume shape has dissipated to leave the pulse plasma. FIG. 6Jdepicts a shape of the plasma flow corresponding to time t₉ where thetemperature drops to the base plasma temperature, the device againgenerates the base plasma flow, which replaces the pulse plasma over thepartial length of the base plasma flow. FIG. 6K depicts a shape of theplasma flow corresponding to time tio where the base plasma flow isdeveloped over its length and the pulse plasma has dissipated, similarto FIG. 6A.

As observed in FIGS. 6A-6K, if the base plasma flow and the pulse plasmaflow are allowed to become fully developed, then both flows may have aneffect on a treated surface, with pulse plasma flow having asubstantially greater effect. When both flows are allowed to develop,the radial expansion of the plasma flow, as depicted in FIGS. 6B-6H, maybe temporary and unstable.

In contrast to FIGS. 5 and 6A-6K, FIGS. 7 and 8A-8E depict generation ofan embodiment of radially expanded plasma flow. FIG. 7 is a plot oftemperature and time of a predominantly radially expanded plasma flowand FIGS. 8A-8E are schematic diagrams of the predominantly radiallyexpanded plasma flow corresponding to the temperature and time plot ofFIG. 7 . FIG. 7 is a plot of temperature and time where a base plasmatemperature has been established at an outlet of a plasma-generatingdevice at time t₀. At time t₁, the plasma temperature at an outlet ofthe plasma-generating device is increased to a pulse plasma temperatureand maintained until time t₃, at which point the temperature isdecreased back to the base plasma temperature until it is raised againat time t₄. FIG. 8A depicts a shape (e.g., volume of plasma flow)corresponding to time to where plasma is heated to a base temperature atthe outlet.

FIG. 8B depicts a shape of plasma flow corresponding to time ti wherepulse plasma flow begins to develop. As a pulse plasma flow frontpropagates, the pulse plasma particles can collide with slower baseplasma flow particles to generate the radial expansion depicted in FIG.8B to form in the proximity of the outlet of a plasma-generating device.FIG. 8C depicts a shape of plasma flow corresponding to time t₂ wherethe pulse plasma flow propagates along a length of the base plasma flowlength so as to create the radial expansion over the length of the baseplasma flow. FIG. 8D depicts a shape of plasma flow corresponding totime t₃ where the base plasma flow begins to form once again with theradially expanded flow from the previous collisions still present. FIG.8E depicts a shape of plasma flow corresponding to time t₄ where thepulse plasma flow is formed again with pulse plasma particles thatpropagate downstream and collide with the particles of the base plasmaflow to generate the radial expansion in the proximity of the outlet.The radially expanded plume extends along the length of the base plasmaflow even at time t₄. In some embodiments, repeating this process maygenerate a predominantly radially expanded plasma flow.

For some applications, a predominantly radially expanded plasma flow mayhave advantages over a continuous plasma flow. For example, a continuousplasma flow may have a width (e.g., radial expansion) that is about twotimes to about four times a diameter of an outlet of a plasma-generatingdevice, while a width (e.g., radial expansion) of a predominantlyradially expanded plasma flow may be greater than that of a continuousplasma flow, e.g., greater than about four times the diameter of theoutlet to about twenty times the diameter of the outlet, including allsub-ranges and values therebetween. Furthermore, a temperaturedistribution along the length of the plasma flow may be more uniform(e.g., may have less variations) for a predominantly radially expandedplasma flow than a continuous plasma flow. These attributes ofpredominantly radially expanded plasma flows may help reduce adverseeffects caused by operator errors due to skill and/or inexperience.Additionally or alternatively, the plasma flows described herein may beused in applications where continuous plasma flows are unsuitable.

In some embodiments, predominantly radially expanded plasma flows may begenerated as a result of interactions of at least two plasma flow (e.g.,a base plasma flow and a pulse plasma flow). Each of the base plasmaflow and the pulse plasma flow in isolation may lack certain desirablequalities associated with predominantly radially expanded flows, buttogether they can generate a predominantly radially expanded flow withsuch desirable qualities. In some embodiments, a predominantly radiallyexpanded plasma flow may be generated by optimizing one or moreparameters of a base plasma flow and pulse plasma flow. First, forexample, a duration of the high energy flow (e.g., a duration of energyabove a predetermined threshold) can be selected to allow the plasmaflow to undergo substantially radial expansion over an entire length orduration of the base plasma flow (e.g., time t₃ shown in FIG. 6D)without transitioning into the axial expansion (e.g., time t₄-t₈ shownin FIGS. 6E-6I). For a given base plasma temperature, decreasing thepulse plasma temperature and increasing the duty cycle may satisfy thisfirst condition. More specifically, for a predetermined base plasmatemperature, the pulse plasma temperature may be selected such the ratioof the speed of sound of the plasma at the pulse temperature to thespeed of sound of the plasma at the base temperature is at most aboutfour, which results in at least a duty cycle of about 0.25. This firstcondition can provide an upper boundary of the pulse plasma temperature.

Second, for example, given a base plasma temperature at the outlet, thepulse plasma temperature may be selected such that the density ratio ofthe two plasmas is at least about two. This second condition can providea lower boundary condition of the pulse plasma temperature and canensure a predetermined scattering effect of plasma particles when thedense and slow-moving base plasma particles are bombarded by the sparseand fast-moving pulse plasma particles.

Third, for example, a base energy duration may be configured such thatthe pulse plasma “catches up” to (e.g., reaches and/or interacts with)the base plasma at a distance about equal to the length of the baseplasma flow. This can reduce the effect of the base plasma flow on asurface being treated and ensure that the surface is treatedpredominantly or only by the radially expanded plasma flow. In someapplications, base plasma flow may be generally undesirable and may bereduced or minimized by configuring a base plasma-pulse plasma cycleperiod. In some embodiments, the base plasma-pulse plasma cycle periodmay be up to about 1 ms.

When pulses of the temperature of the plasma flow at the outlet of apulse-generating device take the form of a rectangular waveform, such asthat depicted in FIG. 9 , a predominantly radially expanded flowsatisfying the above three conditions can be generated for a given baseplasma temperature by setting certain pulse plasma temperature andtiming parameters. For example, FIG. 9 depicts a rectangular pulseincluding a predetermined base plasma temperature of about 3,000 K. Thepulse plasma temperature may be set to about 20,000 K to satisfy thespeed and density ratios relationships given the base plasmatemperature, as described above. Furthermore, a pulse duration t_(p) andoff duration or base duration tb may be set to establish a period t_(t)and duty cycle D. The period t_(t) may be equal to the sum of pulseduration t_(p) and off duration tb. The duty cycle D may be equal to thepulse duration divided by the period, or t_(p)/t_(t). Therefore, asubstantially radially expanded plasma flow may be generated for apredetermined base plasma temperature when the plasma temperature fallsinto a range with a set of predetermined boundary conditions. Theremaining timing parameters may be calculated based on the temperaturevalues, as further described in detail below.

In some embodiments, a method may include applying, to aplasma-generating gas supplied to a plasma-generating device, energythat alternates between being at a base level for a first duration andat a pulse level for a second duration according to a predetermined(e.g., controlled) pattern. In response to applying the energy, a plasmaflow having a directional axis may be generated. In some embodiments,the plasma flow alternating between a base configuration (or a baseplasma flow) and a pulse configuration (or a pulse plasma flow) may bedischarged from the outlet of the plasma-generating device according tothe controlled pattern. In some embodiments, the plasma flow in the baseconfiguration (or base plasma flow) may have (1) a first temperature atthe outlet and (2) a first flow front that advances along thedirectional axis. In some embodiments, the plasma flow in the pulseconfiguration (or pulse plasma flow) may have (1) a second temperatureat the outlet that is greater than the first temperature and (2) asecond flow front that advances along the directional axis at a speedgreater than the first flow front such that a distance traversed by thesecond flow front during the second duration is substantially the sameas a distance traversed by the first flow front during the firstduration and the second duration.

In some embodiments, the plasma flow in the base configuration mayinclude plasma having a first density at the first temperature. Theplasma flow in the pulse configuration may include plasma having asecond density at the second temperature. The first density may be atleast twice the second density.

In some embodiments, the plasma flow in the base configuration mayinclude plasma having a first speed of sound at the first temperature.In some embodiments, the plasma flow in the pulse configuration mayinclude plasma having a second speed of sound at the second temperature.In some embodiments, the second speed of sound may be at most four timesthe first speed of sound.

In some embodiments, the first temperature may be between about 2,000 Kand about 4,000 K. In some embodiments, the second temperature may beless than or equal to about 15,000 K. In such embodiments, if a ratio ofa flow rate G (L/min) of the plasma-generating gas to a diameter d (mm)of the outlet is less than or equal to 100, then a sum of the first andsecond durations may be less than

$100,000*{\frac{d^{4}}{G^{2}}.}$

Alternatively, if the ratio of the flow rate G (L/min) of theplasma-generating gas to a diameter d (mm) of the outlet is greater than100, then a sum of the first and second durations may be less than 5 ms.

In some embodiments, the second temperature may be greater than 15,000K. In such embodiments, if a ratio of the flow rate G (L/min) of theplasma-generating gas to a diameter d (mm) of the outlet is less than orequal to 100, then a sum of the first and second durations may be lessthan about

$5,{000*{\frac{d^{4}}{G^{2}}.}}$

Alternatively, in such embodiments, if the ratio of the flow rate G(L/min) of the plasma-generating gas to a diameter d (mm) of the outletis greater than about 100, then a sum of the first and second durationsmay be less than about 500 μs.

In some embodiments, a length L_(J) and a diameter d_(J) of a radiallyexpanded volume of plasma flow (e.g., shown in FIGS. 1 and 3 ) may bedefined by a set of plasma-generating device parameters including inletgas flow G_(IN), diameter of heating channel d_(H), outlet diameterdour, and temperature and time profile of outlet plasma flow T_(OUT)(t).In particular, the generation of a plasma jet or flow with predominantradial expansion can require a specific or predetermined temperature andtime profile of outlet plasma flow T_(OUT)(t), which may include one ormore of a predetermined frequency of temperature oscillation, baseplasma temperature, pulse temperature amplitude, pulse shape, duration,etc. In general, plasma flow refers to moving particles of gas and caninclude flow embodied as a plasma jet. A plasma jet refers outlet plasmaflow from a device (e.g., a plasma-generating device, such as thosedescribed herein). In some embodiments, parameters such as inlet gasflow and outlet diameter may be constrained by requirements of aspecific application of a plasma-generating device. Therefore, for eachapplication, a plasma jet power needs to be regulated to achieve adesired effect. In some embodiments, the plasma jet power can beestimated as P_(J)=G_(IN)*h(T), where G_(IN) is the inlet gas flow andh(T) is an average enthalpy of the plasma flow. When the outlettemperature and time profile is fixed, the plasma jet power can beregulated by adjusting gas flow G_(IN). Other device parameters that canaffect the plasma jet power can be the outlet diameter d_(OUT) or theheating channel diameter d_(H). The outlet diameter d_(OUT) can provideadjustment of heat flux, and the heating channel diameter d_(H) whendecreased can result in a higher level of inlet pressure, thusincreasing the length of a radially expanded plasma flow. Configurationof such device parameters such as G_(IN), d_(H) and d_(OUT) may beselected to be within a predetermined range and relationship in order togenerate predominantly radial expansion of plasma flow.

In some embodiments, the plasma-generating gas for generatingpredominantly radially expanded plasma flows may be argon or otherinsert gases such as neon, krypton, xenon, radon, combinations thereof,and the like. Depending on the plasma-generating gas used, the differentthermal properties of those gases can impact the different parameterscalculated herein (e.g., sound speed of gas, ratio of sound speed of thegas to density), which in turn can impact the flow profile of the plasmaflow generated, as described in further detail the following sections.

2. Parameters for Generating Radially Expanded Plasma Flows

Predominantly radial expanded plasma flow may be characterized usingtheoretical and experimental relations between input device parameters,such as inlet gas flow G_(IN), diameter of heating channel d_(H), andoutlet diameter d_(OUT), and outlet jet parameters T_(OUT)=T_(OUT)(1).FIG. 10 is a plot of inlet pressure and argon mass flux dependence forsteady laminar flow. In particular, FIG. 10 provides a comparisonbetween the theoretical models for the argon mass flux as a function ofinlet pressure and their practical counterparts for differenttemperatures. For a cylindrical heating channel, the mass flux and theamount of heat added may correspond to the pressure of theplasma-generating gas at an active chamber inlet 112 (FIG. 1 ). For aconstant heating channel diameter d_(H), the flow parameters may berelated by the following equations that include conservation of mass,momentum, energy, and equation of state, respectively:

$\begin{matrix}{{\frac{d\rho}{\rho} + \frac{dU}{U}} = 0} & (1)\end{matrix}$ $\begin{matrix}{{{dP} + {\frac{1}{2}\rho U^{2}\frac{f}{d_{H}}dx} + {\rho UdU}} = 0} & (2)\end{matrix}$ $\begin{matrix}{{{gd}\left( {h + {\frac{1}{2}U^{2}}} \right)} = q} & (3)\end{matrix}$ $\begin{matrix}{P = {Z\rho{RT}}} & (4)\end{matrix}$

where ρ is density, U is plasma flow velocity, P is pressure, f is aMoody friction factor in friction losses of pressure, g is mass flux, his plasma enthalpy, q is added heat, Z is a compressibility factor tocorrect ideal gas equation, R is a gas constant for theplasma-generating gas, and T is the temperature of the plasma-generatinggas.

The solid lines (1010, 1020, 1030) in FIG. 10 correspond toexperimentally measured inlet pressures with controlled gas flow for anargon plasma-generating device, and the dotted lines (1012, 1022, 1032)correspond to calculated inlet pressures. For example, line 1010corresponds to the experimentally measured inlet pressures associatedwith plasma flow at 11,800 K and line 1012 corresponds to the calculatedinlet pressures associated with plasma flow at 11,800 K plasma flow;line 1020 corresponds to the experimentally measured inlet pressuresassociated with plasma flow at 9,200 K and line 1022 corresponds to thecalculated inlet pressures associated with plasma flow at 9,200 K plasmaflow; and line 1030 corresponds to the experimentally measured inletpressures associated with plasma flow at 3,500 K and line 1032corresponds to the calculated inlet pressures associated with plasmaflow at 3,500 K plasma flow. Accordingly, as depicted in FIG. 10 , for awide range of temperatures, the experimental values track the expectedvalues based on the equations described herein.

FIG. 11 depicts a relationship between active chamber inlet pressure andplasma flux at different plasma flow temperatures. In FIG. 11 , the basetemperature 1110 is set to about 3,000 K and the pulse temperature 1120is set to about 15,000 K. For example, a gas flow controller (e.g.,controller 102 depicted in FIG. 1 ) may be configured to supply plasmagenerating gas with a substantially constant flow rate of about 0.6L/min. Under these conditions, generation of about 3,000 K plasma flowwould require about 1 Bar of pressure. For the same flow rate,generation of about 15,000 K plasma flow would require about 3 Bars ofpressure. However, when the pulse plasma flow and the base plasma flowalternate with a duty cycle (e.g., of about 0.6), a pressure Pw of about2.2 Bar may be required. Projecting this pressure onto the corresponding3,000 K base plasma flow graph 110 and 15,000 K pulse plasma flow graph1120 shows that during the base plasma flow, the gas flow rate can beabout 1.32 L/min, and during the pulses the gas flow rate can be about0.42 L/min. However, the gas flow can on average be about 0.6 L/min, andincreasing the temperature can result in increased pressure. Thesubsequent decrease in temperature can result in a decrease or releaseof pressure. In some embodiments, Pw may be represented by the followingequation:

P_(W)=P_(B)+D×(P_(P)−P_(B))   (5)

where D is a duty cycle of pulses, P_(B) and P_(P) are the pressure atthe active chamber inlet when generating the about 3,000 K base plasmaflow and about 15,000 K constant current steady plasma flow,respectively. P_(W) corresponds to working pressure that denotes theresulting inlet pressure in an active chamber of the plasma-generatingdevice when the plasma flow is generated with oscillated outlettemperature with the duty cycle. While the duty cycle in this example is0.6, it can be appreciated that other values for duty cycle can be usedin accordance with the conditions described herein. If the workingpressure P_(W) is a constant and is between P_(B) and P_(P), then therelation between duty cycle D and gas flow may be calculated from thefollowing expression:

$\begin{matrix}{{G_{IN} \times T} = {{G_{P} \times D \times T} + {G_{B}\left( {T - {D \times T}} \right)}}} & (6)\end{matrix}$ $\begin{matrix}{D = \frac{G_{B} - G_{IN}}{G_{B} - G_{P}}} & (7)\end{matrix}$

where G_(IN) is inlet gas flow, T is a period of temperatureoscillation, and G_(B) and G_(P) are the resulting outlet gas flows forbase and pulse outlet temperature, respectively. FIG. 11 depicts theserelationships.

Experimental data confirms the relationship shown in equation (5) fortemperature oscillations having a frequency range between about 10 Hzand about 50 kHz. Thus, in certain applications, given predeterminedbase and pulse temperatures, the working pressure may be tuned bychanging the pulse duty cycle. Accordingly, the temperature oscillationprofile (defined by the base temperature, the pulse temperature, and theduty cycle) can affect the working pressure and can shift resultingpressure towards a predetermined value.

Choking Conditions

In some embodiments, a sufficiently high working pressure level maycause a choking condition in the heating channel where the flow maychoke at a position of the active chamber depending on a shape of theactive chamber and its relationship to the outlet. Oftentimes, thechoking condition occurs at an expansion point. FIGS. 12A-12C areschematic diagrams of choking conditions for example outlets. In FIGS.12A-12C, location 1210 identifies a choking condition location (e.g.,choke point). FIG. 12A depicts an active chamber 1206 having a constantdiameter where the choking condition occurs as the plasma flow isdischarged from the outlet 1212. In FIG. 12A, outlet 1212 serves as anexpansion causing choking condition 1210. In FIG. 12B, the activechamber 1216 expands upstream of the outlet such that the chokingcondition 1210 occurs at the point of expansion. In FIG. 12C, the activechamber 1226 constricts upstream of the outlet such that the chokingcondition 1210 occurs at the outlet 1222. A corresponding chokedvelocity (e.g., sonic speed) may be established if the pressure drop APin the heating portion of active chamber 1206, 1216, 1226 has thefollowing relationship with atmospheric or ambient pressure, Pa:

$\begin{matrix}{\frac{{\Delta P} + P_{a}}{P_{a}} \geq \left( \frac{\gamma + 1}{2} \right)^{\frac{\gamma}{\gamma + 1}}} & (8)\end{matrix}$ $\begin{matrix}{P_{CH} = {{\Delta P} + P_{a}}} & (9)\end{matrix}$

where γ is an adiabatic index, and PCH is absolute inlet pressure ifequation (8) is met. Equation (8) may be used to calculate the criticalstatic pressure at the sonic speed.

Gas Flow Rate

In some embodiments, a plasma-generating device may include a relativelyshort channel configured to heat plasma-generating gas. For theseembodiments, friction may be negligible and need not be considered incalculating the inlet pressure. For the choked condition, thecorresponding equation for mass flow rate G (kg/s) and mass flux g(kg/(m²×s)) may be expressed as follows:

$\begin{matrix}{g = {{4 \times \frac{G}{\pi d_{CH}^{2}}} = {P_{CH} \times \sqrt{\left( \frac{\Upsilon \times \mu}{Z \times R \times T_{CH}} \right) \times \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{\gamma - 1}}}}}} & (10)\end{matrix}$

where Z is a gas compressibility factor, and P_(CH) and T_(CH) stand forthe inlet pressure and temperature of the choked plasma flow,respectively.

Considering the adiabatic index as a weak function of temperature, aflow rate ratio of pulse plasma flow to base plasma flow may beestimated based on Eq. 10 as follows:

$\begin{matrix}{\frac{G_{P}}{G_{B}} = {\frac{g_{P}}{g_{B}} = \sqrt{\frac{T_{B}}{T_{p}}}}} & (11)\end{matrix}$

where T_(B) and T_(P) are base temperature and pulse temperature,respectively. Using Eq. 6, the base pulse flow rate and pulse flow ratemay be evaluated as follows:

$\begin{matrix}{G_{P} = \frac{G_{IN}}{D + {\sqrt{\frac{T_{P}}{T_{B}}}\left( {1 - D} \right)}}} & (12)\end{matrix}$ $\begin{matrix}{G_{B} = \frac{G_{IN}}{{D\sqrt{\frac{T_{B}}{T_{p}}}} + \left( {1 - D} \right)}} & (13)\end{matrix}$

Pulse gas flow rate G_(P) can be less than base gas flow rate G_(B)while inlet gas flow rate G_(IN) is maintained constant. Thus, duringoscillation of outlet temperature, the plasma-generating device can beanalogized to a rapid valve that is open for base plasma flow andpartially closed for pulse plasma flow. For example, if base and pulsetemperatures are about 3000 K and about 11000K, respectively, and dutycycle is about 0.5, the pulse gas flow can be about G_(P)=0.69·G_(IN)and base gas flow can be about G_(B)=1.31·G_(IN). The pulse gas flow maybe less than inlet gas flow and the base gas flow may be more than inletgas flow. As a result, base plasma flow may drain the plasma-generatinggas for the base duration and act as a pressure drain, and pulse plasmaflow may build up pressure in the system for the pulse duration. Forproper operation, the inlet pressure can be maintained constant. Toachieve this, various parameters can be selected such that apredetermined amount of gas is stored in the expansion chamber andtherefore pressure does not drop when the base plasma flow drains thegas. In some embodiments, the gas may be calculated as a product of basegas flow rate G_(B) and base duration T(1-D). In some embodiments, thevolume of expansion chamber may be V_(EXP)=N·G_(B)·T(1-D) where factor Nmay be a number that is about equal to at least 2 to 5 to maintain theinlet pressure.

FIG. 13 is a plot of measured argon plasma flows with fixed mass flux.The dash line 1310 corresponds to the calculated inlet pressure PCHaccording to equation (10). The obtained data reveals that for thevalues of mass flux, g, greater than about 40 kg/(m²s), the inletpressure is higher than the critical value. A relatively high outletstatic pressure may correspond to undesirable effects such as gasembolism for medical applications. Therefore, in some embodiments, thenozzle design depicted in FIG. 12B can be used, which is configured toprevent undesirably high outlet static pressure.

Mach Number

In some embodiments, an adaptive nozzle design may be used to avoid theexcessive outlet static pressure and increase the outlet velocity ofplasma flow. The maximum possible flow velocity that can be achievedwithout expansion of the nozzle is the speed of sound at a given or settemperature of the plasma-generating gas. When a working pressure ishigher than a critical pressure, the outlet flow velocity may achieve aMach number of more than unity (M>1) with an adaptive outlet nozzle. TheMach number can represent the ratio of flow velocity past a boundary tothe local speed of sound, or M=U_(j)/α. At the boundary with chokingconditions, the Mach number may be equal to unity, i.e., M=1. In someembodiments, nozzle expansion may correspond to an increase of Machnumber that results in an increase of flow velocity and decrease ofoutlet static pressure.

The Mach number that can be achieved for a given inlet pressure P_(CH)can be evaluated using the following models. In some embodiments, inletpressure or static pressure can be equal to stagnation pressure (e.g.,associated with total energy) when there is a relatively cold gas flowthat has a low speed. Stated differently, inlet pressure can be equal tostagnation pressure minus dynamic pressure. In particular, the relationbetween pressure ratio (i.e., P_(CH)/P_(α)) and the Mach number forisothermal and isentropic flow models may correspond to Eq. 14 and Eq.15, respectively:

$\begin{matrix}{\frac{P_{CH}}{P_{a}} = {\exp\left( \frac{M^{2}}{\gamma} \right)}} & (14)\end{matrix}$ $\begin{matrix}{\frac{P_{CH}}{P_{a}} = \left( {1 + {\frac{\gamma - 1}{2}M^{2}}} \right)^{\frac{\gamma}{\gamma - 1}}} & (15)\end{matrix}$

These equations show an estimate for the maximum Mach number that can beachieved for a fixed value of working pressure. For example, for aworking pressure of about 5 bar and plasma flow temperature of about7,000 K, the Mach number can be calculated to be about 1.6. Accordingly,an outlet velocity of an adaptive nozzle may be about 1.6 times higherthan the velocity at the boundary with choking conditions. Thecorresponding outlet diameter to achieve the maximum outlet jet velocityand level of static pressure with a given ambient pressure may becalculated based on the following area-Mach number function:

$\begin{matrix}{{f(M)} = {\frac{A_{out}}{A_{ch}} = {\frac{d_{OUT}^{2}}{d_{H}^{2}} = {\left( \frac{\gamma + 1}{2} \right)^{\frac{\gamma + 1}{2{({\gamma - 1})}}}\frac{M}{\left( {1 + {\frac{\gamma - 1}{2}M^{2}}} \right)^{\frac{\gamma + 1}{2{({\gamma - 1})}}}}}}}} & (16)\end{matrix}$

where A_(out) and A_(ch) are outlet area and area of the boundary withchoking conditions, respectively. Static pressure in the outlet plasmaflow may depend on a number of factors, including, for example, inletpressure, outlet mass flux, and nozzle geometry. Depending on thesefactors, the static pressure of the outlet plasma flow or the plasma jetcan be above, equal to, or below ambient pressure.

Velocity

A radial velocity profile may be derived based on a radial temperatureprofile and known outlet Mach number as shown in the following equation:

U_(j)(r)=M·a(T_(OUT)(r))   (17)

In embodiments described herein, a high pulse temperature of plasma flowmay be achieved using electric arc discharge for the heating source byhaving a high ratio of pulse power density. In some embodiments, arelatively small cross-section of a heating channel may be configuredfor a relatively high ratio of pulse power density. In some embodimentssuch as surgical instruments, the size of a plasma-generating device maybe limited and therefore the size of the heating channel d_(H) may beconstrained. Such conditions may require a higher mass flux to provide apredetermined plasma jet power. In embodiments having sizeconstrictions, the choke condition is typically realized in a wide rangeof working parameters of the plasma-generating device. Thus, equationsfor rocket engine design may be used to calculate outlet parameters ofplasma flow that depend on conditions in the heating channel.

In some embodiments, the outlet velocity of a plasma flow is a parameterthat can also be configured to generate a predominantly radiallyexpanded plasma flow. In some embodiments, the outlet velocity of aplasma flow may depend on, but is not limited to, the plasma-generatinggas flow rate, active chamber working pressure, plasma flow temperature,active chamber geometry and structure, and outlet nozzle design.

Based on the outlet thermodynamic parameters described herein, an outletplasma velocity may correspond to a temperature of the plasma flow inthe active chamber and a ratio between ambient pressure and activechamber pressure. For example, if the plasma flow temperature is in therange of between about 3,000 K and about 7,000 K, and the workingpressure is in the range of between about 2 Bar and about 5 Bar, thenthe maximum plasma flow outlet speed may be calculated using thefollowing equation:

$\begin{matrix}{U_{J} = \sqrt{2 \times {h\left( T_{B} \right)} \times \left\lfloor {1 - \left( {P_{a}/P_{CH}} \right)^{\frac{\Upsilon - 1}{\Upsilon}}} \right\rfloor}} & (18)\end{matrix}$

where h(T_(B)) is enthalpy of plasma flow, T_(B) is base temperature,P_(α) is ambient chamber pressure, and P_(CH) is an active chamber inletpressure, and γ is an adiabatic index.

In embodiments described herein, collision of plasma particles are usedto achieve radial expansion of a plasma flow. The higher the probabilityof such collisions, the more significant the radial expansion. In someembodiments, the volume where particles collide defines the resultingactive zone or the plasma flow volume. Several kinematic criteriacontribute to the formation of the optimal conditions for generatingpredominantly radially expanded plasma including the velocity ratio ofcolliding particles, the density ratio of colliding particles, theinteraction zone, characteristic frequencies of temperature and timeprofiles, and the like.

In some embodiments, a “slower” plasma flow comprised of relativelyslow-moving particles may be exposed to “faster” plasma flow comprisedof relatively fast-moving particles to generate predominantly radialexpansion. While the actual plasma flow speed changes along the axis,the slower plasma is slower than the faster plasma in the zone ofinteraction. As described above, base plasma flow may refer to arelatively low intensity flow (e.g., low speed with high density). Pulseplasma flow may refer to a relatively high intensity flow (e.g., highspeed with low density) that catches up and collides with the baseplasma flow.

Plasma Flow Temperature

As used herein, the term “temperature-time profile” may refer to therelationship of the outlet plasma flow temperature to time such as thetemperature and time plots described herein. The temperature-timeprofile reflects the changes in outlet plasma temperature over time. Theterm “temperature-distance profile” may refer to the relationship of theplasma flow temperature to distance from the nozzle along the axis.While the temperature-time profile may be characterized by thetemperature changes at an output of the plasma-generating device, thetemperature-distance profile may be characterized by a dimensionaltemperature distribution at a predetermined time.

FIGS. 14A and 14C are plots of temperature and time of plasma flow(i.e., a temperature-time profile of the plasma flow) at a lowtemperature (about 7,000 K) and a high temperature (about 15,000 K).FIGS. 14B and 14D are plots of distance and time corresponding torespective FIGS. 14A and 14C. In particular, FIGS. 14B and 14D show thedynamics of plasma flow development corresponding to thetemperature-time profiles depicted in FIGS. 14A and 14C, respectively.For example, FIG. 14B depicts the development of laminar flow length fora plasma flow that develops as a result of the temperature-profile pulseshown in FIG. 14A. As shown in FIG. 14B, the pulse duration is r and theplasma flow length increases until reaching a plateau at t=τ_(d) (whichmay be different for different temperatures). The plasma flow fades whenthe pulse finishes (t=τ_(P)). For a fixed nozzle diameter d_(j), theplasma flow length L_(j) may increase with higher temperatures. FIG. 14Bdepicts three distinct stages (e.g., I, II, III) of plasma flowpropagation (e.g., development) as the derivative corresponding tospeed, which in the context of a plasma flow relates to the plasmatemperature. In stage I of FIG. 14B, plasma temperature and speed has aninsignificant decrease and are almost constant as plasma flow propagatesaway from the outlet in the time range (0, τ_(L)). In stage II, theplasma flow has a substantial decrease in temperature and speed in thetime range (τ_(L), τ_(d)). In stage III, plasma flow corresponds to anessentially flat (e.g., horizontal) line, and the temperature drops tothe surrounding temperature with no significant speed associated withthe plasma flow particles. Stage III corresponds to the time range(τ_(d), τ_(p)). After the pulse terminates, the plasma flow rapidlyfades. FIG. 14D has three stages similar to FIG. 14C with similar plasmaflow duration.

FIG. 15A is a plot of temperature and time of a pulsed plasma flow.FIGS. 15B and 15C are plots of temperature and distance of the pulsedplasma flow corresponding to FIG. 15A. In particular, FIG. 15A depictsan oscillating temperature-time profile with base temperature T_(T) andrectangular pulses T_(I). FIGS. 15B and 15C depict twotemperature-distance profiles corresponding to the plasma flow of FIGS.15A. At a low frequency, as depicted in FIG. 15B, base plasma pulses mayreach the maximum jet length and form steady laminar flows 1510 and1512. At time TT, pulse plasma begins to form at the outlet and interactwith the base plasma flow. Under the low frequency conditions of FIG.15B, the pulse plasma flow may also form a steady laminar flow reachingits maximum length. Under such conditions, the plasma flow maycorrespond to predominantly axial expansion with minor (e.g.,insignificant) periods of radial expansion. FIG. 15C depicts a highfrequency condition where the pulses do not have enough time to reachthe maximum length. In this case, the time of interaction between baseplasma flow and pulse plasma flow may increase, thus generating morefavorable conditions for radial expansion.

In some embodiments, at low frequencies, the particles of the pulseplasma flow collide with the particles of the base plasma flow at stageIII of a base plasma flow front propagation, as shown in FIG. 14B andFIG. 15B. If the frequency is increased, the available time for theplasma flow development may decrease and eventually the pulse plasmaflow can collide with base plasma flow at stage II (f>1/τ_(d)). If thefrequency increases to even higher values, then the interaction mayoccur at stage I (f>1/τ_(L)). In this case, the speed of both baseplasma flow and pulse plasma flow may be assumed to be constant. Thevalidity of this assumption as well as frequency relationships isdemonstrated by the temperature-distance profile of a steady laminarplasma flow, applicable to both the base and pulse plasma flows shown inFIG. 16 .

FIG. 16 is a plot of plasma temperature and density profiles along theflow axis for steady laminar flow with constant outlet temperature. InFIG. 16 , the temperature-time profiles are represented as solid lines1610 and 1612, and the density-time profiles are represented as dashedlines 1620 and 1622. Lines 1610 and 1620 are associated with plasma flowhaving a temperature at about 10,000 K, and lines 1612 and 1622 areassociated with plasma flow having a temperature at about 20,000 K.Therefore, the temperature profile 1610 corresponds to a plasma flowhaving a temperature at about 10,000 K at the outlet that remainsrelatively constant between about 5 mm and about 10 mm where the densityof the flow remains relatively low at around 0.05 kg/m³ over the samedistance for such a flow. After the initial drop, the temperature maydecrease with a relatively low gradient. In some embodiments, theduration of stage I may be estimated as

$\tau_{L} \approx {\frac{1}{3}{\tau_{d}.}}$

Since the particle velocity is directly related to temperature, thevelocities of flows may be considered constant for stage I (f>1/τ_(L)).

Plasma Flow Lengths

In some embodiments, the relationship of respective flow lengths mayaffect the interaction zone between a pulse plasma flow and a baseplasma flow. When unrestricted by time, the flow lengths may be based ontemperature, speed, and diameter of plasma flow. In some embodiments,the flow lengths may be controlled by the duty and frequency of pulsesto optimize radial expansion. In some embodiments, the flow lengths maybe substantially equal to maximize the interaction zone of the baseplasma flow and pulse plasma flow. For a predetermined base plasma flowtemperature and pulse plasma flow temperature, the duty of pulses andvelocity ratio of target and initiator plasma may be adjusted such thatthe base plasma flow length and pulse plasma flow length aresubstantially equal. More specifically, target plasma can be plasmahaving high density and low temperature, e.g., plasma with energy andpower that is minimized. During plasma generation, initiator plasma canbe generated within a plasma-generating device and used to generate aplasma jet. Accordingly, initiator and target plasma can be generatedduring sequential time periods (e.g., first, second) of a plasma flowdevelopment cycle to produce a radially expanded plasma flow. Targetplasma can create volume for interacting with high speed and highenergy/power plasma flow but can also correspond to axial plasma flowand narrow, low energy, plasma flow concentrated in relatively high heatflux. It is therefore desirable to reduce or minimize a duration oftarget flow to avoid such negative impacts of target flow.

Kinematic criteria may be formulated in case of constant velocities,e.g., when base-pulse plasma flows interaction occurs at stage I. FIG.17 illustrates three phases of plasma flow development during a singleperiod. For example, a temperature pulse duty cycle D=0.5 and velocitiesratio U_(pulse)/U_(base)=2, where U_(pulse) and U_(base) are thevelocities of outlet temperature of pulse and base plasma flows,respectively. The base plasma flow and the pulse plasma flow can havethe same maximum length (L=U_(base)T=U_(pulse) t_(pulse), wheret_(pulse) is the temperature pulse duration and T is the periodduration).

In a first phase, the base plasma flow may not be affected by the pulseplasma flow. The duration of this phase may be T/2. In a second phase,the pulse plasma flow may interact with some part of base plasma flow.At

${t = {\frac{3}{4}T}},$

half of the length may be affected by the pulse plasma flow, but thenext quarter of length may be occupied by the predominantly axial baseplasma flow. In a third phase at t=T, all of the volume may be affectedby the pulse plasma flow. As shown in FIG. 17 , a degree of radialexpansion may depend on a distance from the outlet.

The overlap between the base plasma flow and the pulse plasma flow maycorrespond to a first approximation for estimating a ratio of radiallyto axially propagated plasma. FIG. 18 is a graphical illustration ofsuch an approximation. FIG. 18 is a plot of length and time ofinteractions of low and high temperature plasma flow. The vertical linesin FIG. 18 correspond to an axial gradient of a combined plasma flow.The horizontal lines correspond to a radially expanded gradient of thecombined plasma flow. A spacing between the lines correspond to density,i.e., the larger the space between the lines, the lower is the densityand the darkness of the lines corresponds to the velocity, with darkerlines representing higher velocity. FIG. 18 shows an axial cross-sectionof an active zone and plasma type as a function of time (for two timeperiods). During one time period, there is an area of axial base plasma(e.g., thick sparse vertical light lines), and an area where the targetand initiator plasma occupy the same volume. FIG. 18 further illustratesthe axial and radial components at various times and distances from theoutlet. The collision probability inside a predetermined area of thetarget-initiator intersection may depend on a set of parameters.However, for a first approximation, the radial to axial ratio may beestimated as an intersection area to axial area ratio.

FIG. 18 illustrates a front 1800 of the base plasma flow and front 1810of the pulse plasma flow. In some embodiments, the probability ofcollision and consequent radial expansion close to the outlet may behigh when the pulse plasma flow has started. As the pulse plasma flowpropagates over a distance away from the outlet, the probability ofcollision may increase. For an arbitrary time i during the first periodshortly after the pulse plasma flow is initiated, the probability ofcollision and the degree of radial expansion is high at point 1820 closeto the outlet. Since the pulse plasma has not “caught up” completely atpoint 1830, the active zone may be filled predominantly with the baseplasma flow with a low chance of collision. However, even further fromthe outlet at the same time at point 1840, the active zone may be filledwith predominantly radially expanded plasma from the previousinteraction between the base plasma flow and pulse plasma flows from theprevious period that has not yet dissipated into the surroundingenvironment or been “pushed” out by the base plasma flow. In FIG. 18 ,there is no distance where the base plasma flow operates by itself orwhere the pulse plasma flow operates by itself. In some embodiments, therespective temperatures, the period, and the duty may be optimized toprevent such occurrences.

For comparison, FIGS. 19 and 20 illustrate embodiments where a baseplasma flow length is longer and the pulse plasma flow does not extendto the distal-most portions of the active zone (e.g., due to thesub-optimal selection of the low and high temperatures, period, and dutycycle). As a result, there may be a tail of base plasma flow. FIG. 19 isa schematic diagram of plasma flow with oscillating outlet temperature.The maximum length of the target may be greater than the maximum lengthof the initiator. FIG. 20 is a plot of length and time of interactionsof relatively low and high temperature plasma flow.

For further comparison, FIGS. 21 and 22 illustrate an instance where thepulse plasma flow overshoots the base plasma flow leaving the axialpulse plasma operating at the distal end of the active zone (e.g., dueto the sub-optimal selection of the low and high temperatures, period,and duty cycle). FIG. 21 is a schematic diagram of plasma flow withoscillating outlet temperature. FIG. 22 is a plot of length and time ofinteractions of relatively low and high temperature plasma flow withhigh frequency pulses. Comparing FIGS. 17 and 18 with FIGS. 19-22 , thehighest radial to axial ratio may correspond to the selection ofparameters shown in FIGS. 17 and 18 , where the length achieved by thebase plasma flow during a base plus pulse period is equal to the lengthachieved by the pulse plasma flow during the pulse period. Therefore,the optimization of a set of parameters corresponds to increasing theradial expansion probability based on the lengths of the base plasmaflow and pulse plasma flow being substantially equal under suchconditions.

In some embodiments, equal length may be achieved based on a duty ofpulses and velocity ratio. In particular, parameters can be selectedsuch that a length of a base plasma flow during the period T is the sameas the length of the pulse plasma flow during the temperature pulseperiod, as given by:

$\begin{matrix}{L = {{U_{base}T} = {U_{pulse}t_{pulse}}}} & (19)\end{matrix}$ $\begin{matrix}{\frac{U_{base}}{U_{pulse}} = D} & (20)\end{matrix}$

where U is the speed of the respective flows and D is the duty cycle.

For example, a suitable pulse plasma flow temperature can be selectedbased on a predetermined duty cycle and base plasma flow temperature, ascalculated using the equations above. For example, the axial/radialcomponent ratio may be estimated for various duty values as shown inFIG. 18 . Further calculations may be based on FIGS. 23A-23Cillustrating plots of radial oscillation ratio and length in aninteractive volume of plasma flow.

As depicted in FIGS. 23A-23C, a predominant radial oscillation may occurin the active zone when a duty cycle of the temperature pulses D>0.25.In some embodiments, a duty cycle of less than about 0.25 may notprovide sufficient radial expansion for some medical applications. Insome embodiments, a duty cycle of about 0.25 corresponds to an upperboundary condition on the temperature/speed ratio of a base plasma flowand pulse plasma flow. FIGS. 23A-23C illustrate that a higher ratio ofbase plasma flow and pulse plasma flow intersection may be achieved atrelatively higher duty values. Additionally or alternatively, averagingthe radial and axial components per one period of outlet temperatureoscillation may provide a lowest radial ratio in proximity to the outletand provide a highest radial ratio at a distal end of the active zone ofthe plasma flow. Such a distribution is consistent with a bottle-shapedplasma flow shown in FIG. 3 . In such cases, the plasma flow diametermay be thinner at a proximity of the outlet due to the higher fractionof axially propagated plasma in this area.

Since velocity is a function of plasma temperatures, the criteria forequal length of plasma flows may be expressed as a function oftemperatures, given by:

$\begin{matrix}{\frac{U_{base}\left( T_{base} \right)}{U_{pulse}\left( T_{pulse} \right)} = D} & \left( {20a} \right)\end{matrix}$

When choking conditions are met, this ratio may be replaced by the soundspeed ratio for a choked flow. Alternatively, when choking conditionsare not met, this ratio can be calculated based on Rayleigh conditions.The Rayleigh conditions (e.g., propagation according to Rayleigh waves)provide a simplified model for calculating inlet and outlet parametersfor gas flow heated in a channel.

FIG. 24 is a plot of target-initiator velocity ratio and pressure forRayleigh flow and choked flows. FIG. 24 illustrates a velocity ratio asa function of inlet pressure P_(inl), where P_(ch) corresponds to achoked pressure. A velocity ratio may be calculated as a sound speedratio for argon. Experimentally measured outlet velocities at variousinlet pressures for argon at plasma flow temperatures of about 4,000 K,about 5,000 K, and about 10,500 K, and Rayleigh conditions may be usedto calculate the presented velocity ratio for Rayleigh flow, as shown inFIG. 24 . The plasma flow temperature may be measured using acalorimetry probe inserted in plasma flow. The velocity ratio for a widerange of base plasma and pulse plasma flow temperatures may be assumedconstant for the following analysis as the ratio provides a closeapproximation for both the Rayleigh flow and choked flows. Therefore,the sound speed ratio may correspond to an equal length of the twoflows, as given by:

$\begin{matrix}{\frac{a\left( T_{base} \right)}{a\left( T_{pulse} \right)} = D} & \left( {20b} \right)\end{matrix}$ $\begin{matrix}{a = \sqrt{\frac{\gamma RT}{M}}} & (21)\end{matrix}$

where α is the speed of sound as a function of temperature, γ is theadiabatic index, and M is a molar mass of the plasma generating gas.

As described herein, the duty cycle D of the pulse plasma flowtemperature may correspond to a fraction of radial expansion. Equation(20b) may be used to evaluate fixed values of the duty cycle. The dashedlines shown in FIG. 25 correspond to duty contours (e.g., level curves)that meet equation (20b). The sound speed of the argon plasma is awell-known quantity. A thickness of the dashed lines may illustrate theduty cycle value (i.e., thicker lines correspond to higher values ofduty cycle). To decrease a higher ratio of axial plasma flow, an upperlimit for the pulse plasma flow temperature may be introduced. Thislimit may depend on a base plasma flow temperature. In some embodiments,a duty cycle D=0.25 may be used as reference value to estimate an upperlimit of pulse temperature T_(pulse) ^(max) as a function of base plasmaflow temperature T_(T):

$\begin{matrix}{\frac{a\left( T_{base} \right)}{a\left( T_{pulse}^{\max} \right)} = \left. {{0.2}5}\Rightarrow{T_{pulse}^{\max}\left( T_{base} \right)} \right.} & (22)\end{matrix}$

In some embodiments, for a fixed base plasma flow temperature, the pulseplasma flow temperature may be lower in order to reach higher values ofduty. However, if the temperature difference between relatively high andlow intensive plasma flows is small, then the probability of collisioninside the target-initiator intersection area may be low as well. Forexample, if the duty is about D≈1, then there is almost no differencebetween base plasma flow and pulse plasma flow. Instead of having thehighest radial fraction, the flow may form an axial laminar jet.Therefore, the probability of collision needs to be considered todetermine optimal conditions. In some embodiments, the collisionprobability may be based on a local concentration of target andinitiator particles and velocity ratio.

As discussed above, FIG. 16 depicts an embodiment of plasma densityprofile along a flow axis. The density may be determined based on atemperature-distance profile and the relationship between the densityand temperature (which may be found in literature). The density mayincrease as the plasma flow temperature decreases along the axis. Ahigher probability of collision may be achieved if the ratio of speed ofthe two plasma flows and the ratio of density of the two plasma flowsare relatively high. In some embodiments, a plasma density ratio may becorrespond to higher collision probability since both the velocity anddensity depend on temperature. Similarly, equation (20b) may beevaluated for various fixed values of density ratios. The solid lines inFIG. 25 may represent constant density ratios. The density ratioscalculated for argon plasma are based on literature values. Thethickness of the solid lines further indicate a density ratio wherethicker lines correspond to a higher density ratio. In the same manner,a lower limit of the pulse plasma flow temperature may be introduced toavoid lower collision probability in the active zone. In someembodiments, a density ratio of about 2 may be a reference value used toestimate a lower limit of pulse temperature T_(pulse) ^(min), given by:

$\begin{matrix}{\frac{\rho\left( T_{base} \right)}{\rho\left( T_{pulse}^{\min} \right)} = \left. 2\Rightarrow{T_{pulse}^{\min}\left( T_{T} \right)} \right.} & (23)\end{matrix}$

For a predetermined base plasma flow temperature, the pulse plasma flowtemperature may be at least as high so to have at least a density ratioof about two.

FIG. 25 is a plot of duty and density ratio relationships for radialexpansion with argon as a plasma generating gas. As shown in FIG. 25 ,both criteria for a higher duty and a higher density ratio correspond toboundary conditions on the region where radial expansion is prevalent.At the same time, the criteria have opposite requirements. For example,the pulse plasma flow temperature can be maximized for a predeterminedtarget temperature in order to increase collision probability. However,the pulse plasma flow temperature if minimized increases an interactionzone. Therefore, there can be an optimal area with a higher fraction ofradial expansion. In other words, for a predetermined base plasma flowtemperature, a range of pulse plasma flow temperatures may provide a setof predetermined (e.g., optimal) conditions.

FIG. 26 is a plot of target temperature and initiator temperature forpredominant radial expansion. FIG. 26 illustrates an arbitrary regionfor predominant radial expansion. For example, a base plasma flowtemperature may be about 4,000 K. In some embodiments, a predetermined(e.g., sufficient) radial expansion may be generated with a pulse plasmaflow temperature in a range between about 7,500 K and about 26,500 K. Insome embodiments, the pulse plasma flow temperature may be in a rangebetween about 11,000 K and about 26,000 K. In some embodiments, therange may be between about 12,500 K and about 20,000 K. In someembodiments, the range may be between about 14,000 K and about 17,500 K.A set of pulse plasma flow temperature ranges may be determined usingFIG. 26 for a predetermined base plasma flow temperature. The intensityof shading in FIG. 26 corresponds to a fraction of radial expansionbased on duty and density ratio criteria, with darker shadingrepresenting a higher (more desirable) fraction.

FIG. 25 illustrated density and speed ratios calculated based onthermodynamic parameters of argon as plasma generating gas. Similar datamay be obtained for other gases or their mixtures. For example, FIG. 27illustrates density and speed ratios based on thermodynamic parametersof air as plasma generating gas. The dashed lines of FIG. 27 indicateduty contours (level curves) that meet the criteria of equation (20b),and the solid lines represent constant density ratios. The densityratios are based on air densities known from literature. For simplicity,the speed ratio was estimated assuming that adiabatic index is a weakfunction of temperature. Accordingly, the speed ratio is evaluated as aratio of square roots of the corresponding temperatures. Similarconclusions about optimal region with prevalent radial expansion arevalid for air or other gases or mixtures since various gases have thesame temperature tendencies of thermodynamic parameters.

FIG. 28 is a plot of plasma flow pressure and inlet pressure includingexperimental data of dynamic pressure of pulse plasma flow and baseplasma flow. In some embodiments, the base temperature may be about3,500 K and pulse temperature may be about 11,800 K. In someembodiments, the density ratio ρ(T_(base))/ρ(T_(pulse)) may be about 5and a velocity ratio U(T_(pulse))/U(T_(base)) may be about 1.8. Thedynamic pressure of base plasma flow may be higher than the dynamicpressure of pulse plasma flow. As a result, the base plasma flow maydisplace the residual plasma flow without mixing and filling the volumewith base plasma flow. The higher dynamic pressure of base plasma flowmay be positive since it may reset the conditions for each repetition ofbase and pulse plasma flows. Therefore, at the start of a new outlettemperature oscillation cycle, the outlet base plasma flow may not beaffected by previous pulse plasma flow. Furthermore, the kinematiccriteria may not depend on the number of base-pulse flow repetitions.

However, the kinematic model described herein may have limitationsrelated to a relationship between input device parameters and acorresponding outlet temperature-time profile, as described in moredetail herein. In the kinematic model, the velocity ratio of base topulse plasma flow may be used to derive a criteria for radial expansion.The absolute value of velocity also implies certain restrictions. Forexample, if the input parameters such as inlet gas flow and outletdiameter result in a considerably low value of outlet velocity, then theplasma jet may not form or “fade away” within a predetermined (e.g.,short) distance due to the cooling of the plasma flow. Therefore, apredetermined minimum velocity of plasma jet may be required to achievepredetermined plasma jet length. In some embodiments, a ratio of lengthto outlet diameter may be about 50 to about 100 for a laminar plasma jet. In some embodiments, a minimum plasma ratio L/d_(out) of about 25may be used to formulate limitations for relationships between inputparameters.

In some embodiments, the cooling of a plasma jet with constant outlettemperature may be estimated based on the following equations for anoutlet plasma jet in a laminar mode. For example, the plasma jet mayhave a cylindrical shape with uniform radial temperature distribution.An axial temperature of the jet may decrease due to diffusion of airflow inside the side walls of the plasma jet. The incoming air flow maybe proportional to a surface area of the plasma j et walls. In someembodiments, the axial temperature gradient may be calculated asfollows:

$\begin{matrix}{{G_{IN}C_{p}\frac{dT}{dz}} = {{- g_{air}}\pi d_{OUT}h_{air}}} & (24)\end{matrix}$

where Cp is a heat capacity of plasma, hair is air enthalpy, and g_(air)is air flux per unit area. The plasma jet length may be derived and maybe given by:

$\begin{matrix}{L_{j} = {\frac{G_{IN}}{\pi d_{OUT}}\frac{1}{g_{air}}{\int_{T_{a}}^{T_{out}}{\frac{C_{p}}{h_{a}}{dT}}}}} & (25)\end{matrix}$

where T_(out) and T_(a) are outlet temperature and thresholdtemperature, respectively, that define the plasma jet length.

In this demonstrated model, laminar plasma flow may correspond to aplasma jet length being proportional to an inlet gas flow length andinversely proportional to an outlet diameter. If the conditions forlaminar flow are not met, then the jet length cannot be approximatedusing Equation 25.

FIG. 29 is a plot of plasma jet length and inlet gas flow includingexperimental data of plasma jet length dependence on inlet gas flow. Atrelatively lower gas flow rates, the plasma flow may be in a laminarmode, and the plasma jet length be proportional to an increase of flowrate. At predetermined gas flow values, the plasma jet length may reachits maximum. Plasma flow may immediately shift to a turbulent mode(2910) with an abrupt drop of jet length or may have a transition region(2920) where the jet length slowly decreases, as shown in FIG. 29 .Transitional region (2920) may include a relatively wide range of gasflow rates for predetermined parameters. For example, for an outletdiameter of about 0.5 mm and an outlet temperature of about 12,200 K,the maximum jet length may correspond to a gas flow of about 0.17l/minand L/d_(out) of about 90. In some embodiments, the ratio L/d_(out) maydecrease to about 60 when the flow rate increases about three times. Atransitional region of plasma jet having a predetermined ratio L/d_(out)may be used for radial expansion of the plasma jet since its behavior isnot substantially different from laminar mode and the conditions of thedescribed kinematic model may be met.

In some embodiments, for interpolation of experimental data for variousoutlet diameters, temperature and inlet gas flow, the followingempirically derived equation is given:

$\begin{matrix}{L_{j} = {\frac{A^{*}\left( T_{out} \right)}{d_{OUT}^{p}}G_{IN}}} & (26)\end{matrix}$

where A* (T_(out)) is a function of temperature that may be smoothlyinterpolated between measured values for a predetermined range oftemperatures.

Equation 26 uses empirical index p for outlet diameter to addressnonuniform radial distribution of temperature in the plasma jet. Asdiscussed herein, a plasma jet ratio L/d_(out) may be more than 25 insome embodiments. Thus, a maximum outlet diameter for the fixed value ofinlet gas flow and outlet plasma temperature may be given by:

$\begin{matrix}{d_{OUT}^{\max} = \sqrt[{p + 1}]{\frac{G_{IN}{A^{*}\left( T_{out} \right)}}{25}}} & (27)\end{matrix}$

FIG. 30 shows dependence of maximum outlet diameter on inlet gas flowfor various outlet temperatures. In some embodiments, the maximumdiameter may be higher for a higher temperature. However, gas flow ratesfor pulse plasma and base plasma for oscillating outlet temperature maynot be equal to the inlet gas flow rate G_(IN), as shown in Equation 27.The actual gas flow rate for pulse plasma may be lower than for baseplasma, as shown in Equations 12 and 13. The maximum outlet diameter maylimit the minimal velocity of the plasma jet. In some embodiments, theaverage outlet velocity may be estimated based on the gas flow rate:

$\begin{matrix}{\left\langle U_{\min} \right\rangle = \frac{G_{IN}}{\rho\frac{{\pi\left( d_{OUT}^{\max} \right)}^{2}}{4}}} & (28)\end{matrix}$

In some embodiments, the radial distribution of velocity for a smalloutlet diameter may be estimated as parabolic, and the axial velocitymay be related to an average velocity by the expression U_(axial)=1.5U_(average). A more accurate estimation of a relation between axial andaverage velocities may be based on a radial distribution of outlettemperature. In some embodiments, the relation between axial and averagevelocities may be calculated using Eq. 17:

$\begin{matrix}{\frac{U_{average}}{U_{axial}} = \frac{\frac{8}{d_{out}^{2}}{\int_{0}^{d_{out}/2}{{a\left( {T(r)} \right)}{rdr}}}}{a\left( T_{axial} \right)}} & (29)\end{matrix}$

In some embodiments, ranges for the period of outlet temperature-timeprofile may be determined based on minimal jet velocity conditions. Asdescribed herein, the period of temperature oscillation may be less thana development time of the plasma jet. In some embodiments, the maximumduration of a base plasma or pulse plasma may be limited by the timenecessary to form the plasma jet having a maximum length. In someembodiments, the maximum plasma jet length with predominant radialexpansion for the minimal velocity may be L=25* d_(OUT). Assuming thatthe average axial pulse plasma flow speed U_(pulse) ^(a) may be aboutone half of the pulse plasma speed at the outlet, then the pulse plasmaflow length may be estimated as L=D * U_(pulse) ^(a)* T=0.5* D *U_(pulse) * T. Thus, the period restrictions may be given by:

$\begin{matrix}{T \leq \frac{25*d_{OUT}}{D*0.5*U_{pulse}}} & (30)\end{matrix}$

Combining with Eq. 28, the estimation of period may be rewritten as:

$\begin{matrix}{T \leq \frac{\pi\rho{A^{*}\left( T_{out} \right)}}{d_{OUT}^{p}}} & (31)\end{matrix}$

FIG. 31 is a plot of dependence of maximum period on outlet diameter forvarious outlet pulse temperatures. FIG. 32 is a plot of dependence ofmaximum period on outlet pulse temperature. FIG. 33 is a plot ofdependence of minimum frequency on outlet pulse temperature. For a fixedoutlet diameter and a range of pulse temperatures, FIGS. 32 and FIG. 33illustrate the maximum period and corresponding minimum frequency ofoutlet temperature oscillations to provide conditions for radialexpansion of resulting plasma jet.

It should be noted that the obtained restrictions apply where the plasmaflow is in a laminar mode (e.g., laminar) and in certain cases in atransition mode for a set of predetermined input parameters. Table 1lists a set of period and frequency relationships for varioustemperatures.

TABLE 1 Maximum period and minimum frequency relationships. T_(out), K13,000 K 18,000 K 22,000 K 13,000 K 18,000 K 22,000 K d_(OUT), mmT_(max) T_(max) T_(max) f_(min) f_(min) f_(min) 0.5  170 μs  135 μs  140μs  5.9 kHz  7.4 kHz  6.9 kHz 1  370 μs  300 μs  320 μs  2.7 kHz  3.4kHz  3.1 kHz 5  2.3 ms  1.9 ms   2 ms 430 Hz 540 Hz 500 Hz 10  5.1 ms 4.1 ms  4.4 ms 190 Hz 240 Hz 230 Hz 25 14.6 ms 11.7 ms 12.6 ms  70 Hz 90 Hz  80 Hz

In some embodiments, conditions for a flow to remain laminar may bebased on the Reynolds number. The Reynolds number, Re, corresponds towhether a flow tends to be laminar or turbulent. In some embodiments,the Reynolds number for output parameters of the plasma flowing from aplasma-generating device may be given by:

$\begin{matrix}{{{Re} = \frac{g_{out}d_{OUT}}{\mu}},} & (32)\end{matrix}$

where g_(out) is outlet plasma mass flux, μ is the dynamic viscosity ofplasma, and d_(OUT) is the outlet diameter.

In some embodiments, for cylindrical flows, which may be preferable forcertain applications, Re*=2000. In a real plasma-generating device,other factors may introduce fluctuations of generating parameters. As aresult, reducing the Reynolds number may correspond to a turbulent flowtransition. In some embodiments, a critical Reynolds number may be inrange between about 200 and about 2000.

In some embodiments, the fixed outlet temperature and the Reynoldsnumber may be proportional with a value of outlet diameter based on acomparison of equations 27 and 32. As a result, at a predetermined valueof a maximum outlet diameter and corresponding inlet gas flow rate, aReynolds number may exceed a threshold (e.g., critical value) for alaminar mode. Thus, for a predetermined outlet temperature, a maximumoutlet diameter and relatively higher diameter values may results inturbulent flow. For example, for temperatures in a range between about13,000 K and about 22,000 K, and a critical Reynolds number of 2,000,the maximum possible outlet diameter may be about 130 mm and about 30mm.

FIG. 34 is a plot of dependence of maximum outlet diameter on outletpulse temperature, according to an embodiment. For example, FIG. 34illustrates a maximum outlet diameter based on Eq. 27 when a Reynoldsnumber reaches a value of about 2,000. For higher values of outletdiameter, the resulting plasma flow is in an undesirable turbulent mode.

For a predetermined outlet diameter and outlet plasma temperature, aReynolds number may limit the maximum mass flux for laminar flow.Alternatively, the mass flux may be based on gas flow rate and outletdiameter. Thus, Eq. 32 may be given by:

$\begin{matrix}{{Re} = \frac{G}{\frac{\pi d_{OUT}}{4} \cdot \mu}} & (33)\end{matrix}$

where G is a gas flow rate which is equal to inlet gas flow rate G_(IN)in case of constant outlet temperature.

In some embodiments, the actual gas flow rate may be separatelycalculated for pulse plasma and base plasma for cases involvingoscillating outlet temperature, as shown in Equations 12 and 13. Adynamic viscosity μ may be defined by a plasma temperature. According toEq. 33, there may be a maximum gas flow rate corresponding to thepredetermined outlet diameter and plasma temperature.

FIG. 35 is a plot corresponding to a critical gas flow rate for Reynoldsnumber of about 2000. In some embodiments, outlet gas flow may be lessthan a calculated critical gas flow rate to avoid turbulent mode ofplasma flow. As illustrated in FIG. 35 , a maximum gas flow rate mayincrease with higher outlet diameters. Combining Equations 12, 13, and33, a maximum inlet gas flow rate may be limited to avoid turbulent modebased on the following equations:

$\begin{matrix}{G_{IN} < {{Re}^{*} \cdot \frac{\pi d_{OUT}}{4} \cdot {\mu\left( T_{base} \right)} \cdot \left( {{D\sqrt{\frac{T_{B}}{T_{p}}}} + \left( {1 - D} \right)} \right)}} & (34)\end{matrix}$ $\begin{matrix}{G_{IN} < {{Re}^{*} \cdot \frac{\pi d_{OUT}}{4} \cdot {\mu\left( T_{pulse} \right)} \cdot \left( {D + {\sqrt{\frac{T_{P}}{T_{B}}}\left( {1 - D} \right)}} \right)}} & (35)\end{matrix}$

In some embodiments, inlet gas flow may have a lower limit defined by aminimum working pressure for maintaining a plasma flow. Based on Eq. 10,the lower limit may be estimated based on a mass flux in the heatingchannel. Experimental data may suggest that a mass flux of at leastabout 10 kg/m²s is needed to generate laminar plasma flow. Thus, theminimum inlet gas flow rate may be given by:

$\begin{matrix}{G_{IN} < {K \cdot \frac{\pi d_{H}^{2}}{4} \cdot \left( {D + {\sqrt{\frac{T_{P}}{T_{B}}}\left( {1 - D} \right)}} \right)}} & (36)\end{matrix}$

where K is an empirically measured constant of about 10 kg/m²s, andd_(H) is a diameter of a heating channel.

In some embodiments, the heating of base plasma by pulse plasma in thearea of overlap may be a parameter of a base-pulse plasma flowinteraction model. For example, the collision probability may rapidlydrop when a difference in the flow speed is not substantial. This may beanother reason why the collision probability drops when the base-targetinteraction occurs in stage III. An energy balance equation for the baseplasma flow heated by the pulse plasma flow electrons may be given by:

$\begin{matrix}{{\rho C_{P}\frac{dT}{dt}} = {\frac{3}{2}\delta{vn}_{e}{k\left( {T_{i} - T} \right)}}} & (37)\end{matrix}$

where ρ is the density of the base plasma, C_(p) is heat capacity of thebase plasma, δ is the average fraction of energy that an electrontransfers to a colliding heavy particle of the base plasma flow, n_(e)is the electron density of the pulse plasma flow, and k is the Boltzmannconstant.

For a boundary condition: t=0; T(0)=T_(base); and a=ρC_(P);

${b = {\frac{3}{2}{kvn}_{e}\delta}},$

T(t) may be given by:

$\begin{matrix}\left. {{T(t)} = {{T_{pulse}\left\lbrack {1 - \exp^{({{- \frac{b}{a}}t})}} \right\rbrack} + {T_{base}\exp\left( {}^{{- \frac{b}{a}}t} \right.}}} \right) & (38)\end{matrix}$

A duration of time tF to increase the temperature of target flow to 2TTmay be given by:

$\begin{matrix}{t_{F} = {{{- \frac{a}{b}}{\ln\left( \frac{T_{pulse} - {2T_{base}}}{T_{pulse} - T_{base}} \right)}} \approx \frac{0.2 \times \rho \times C_{P}}{k \times \delta \times v_{ea} \times n_{e{pulse}}}}} & (39)\end{matrix}$

In some embodiments, the time period tF may be a characteristic time toheat the base plasma flow, and may thereby significantly decrease thecollision probability. In some embodiments, the minimum frequency toavoid heating of target plasma flow may be estimated based on the aboveequations. In some embodiments, the calculated minimum frequency may bea function of base plasma flow temperature as illustrated in FIG. 36 .

FIG. 36 is a plot corresponding to frequency relationships to avoidsignificant heating of low intensity plasma. The curves shown in FIG. 36are calculated for pulse plasma flow temperatures corresponding to a setof density ratios. In some embodiments, the heating of base plasma bypulse plasma occurs in the area of overlap. When radial expansionconditions are met, the affected base plasma particles may propagateradially to reduce interaction with pulse plasma. As a result, theactual characteristic time of when a difference between base plasma andpulse plasma becomes insufficient to provide the desired degree ofradial expansion may be expected to be higher than the time obtained inEq. 39. The experimental data for an outlet diameter between about 0.5mm and about 1.5 mm shows radial expansion of a plasma jet for frequencyof at least about 4 kHz.

The kinematic criteria described herein has two underlying assumptionsof a rectangular temperature-time profile and the occurrence ofbase-pulse plasma flow interactions at stage I of front propagation(f>1/τ_(L)). These conditions may not be optimal for generatingpredominant radial expansion of the plasma flow. In some embodiments,maximizing the collision probability (characterized by the densityratio) and maximizing the interaction zone of the two flows(characterized by the pulse duty cycle of rectangular pulses) mayincrease the predominant radial expansion of the plasma flow. However,maximizing both features simultaneously may be difficult due to impliedconstraints. However, experimental results may improve parameteroptimization.

In some embodiments, density profiles for laminar base plasma flow andpulse plasma flow may be compared, as shown in FIG. 16 . The densityratio may increase substantially in a distal end of the active zone. Asa result, the density ratio in this region may be increased while apulse plasma flow outlet temperature is maintained, to thereby satisfyan equal length condition of the plasma flows. In some embodiments, thepulse plasma flow may collide with base plasma flow at stage II or IIIof the base plasma flow front propagation, i.e. at lower frequencies(see FIGS. 37B and 37C). Interaction at stage III may be ignored forpredominant radial expansion because the base plasma flow has mixed withair at stage III. However, optimizing parameters in this manner mayincrease the probability of collision at stage II.

In some embodiments, a temperature-time profile may have a more complexwaveform than a rectangular pulse in order to increase an interactionzone and maintain a relatively high density ratio of base plasma andpulse plasma flows. FIGS. 38A-38F illustrate several examples ofillustrative temperature-time profiles configured to increase radialexpansion while minimizing the time-volume of the axial component of thebase plasma flow. In FIG. 38D, the pulse may include several decreasingtemperature steps. Initially, the pulse has a relatively hightemperature to ensure a relatively high density ratio. Then, the pulsetemperature may decreases by several smaller steps. FIG. 38A depicts thecorresponding axial plasma component in the active-zone/timecoordinates. The pulse plasma flow front speed may decrease, thusefficiently prolonging the time when the pulse plasma flow reaches thelength of the target plasma flow. Therefore, the volume of thebase-pulse plasma flow overlap may increase while maintaining arelatively high density ratio.

In some embodiments, an ideal temperature pulse curvature may: (1)increase an effective value of duty

$D_{eff} = \frac{\tau_{p}}{T}$

to reduce the zone of axially propagated base plasma flow;

and (2) increase the collision probability of plasma particles atvarious distances from the outlet by keeping the relatively high densityratio at different distances from the outlet during pulse plasma flowfront propagation. FIG. 38E illustrates another pulse of a substantiallyparabolic shape that gradually goes from a maximum value to apredetermined value between the base plasma flow temperature and thepulse plasma flow temperature, and then steps down to the base plasmaflow temperature. The corresponding axial plasma component is shown inFIG. 38B. In another example, the pulse may have the shape shown in FIG.38F. The base plasma flow may be formed by a series of smaller pulses.After the initial spike to the pulse plasma temperature, the temperaturemay undergo a number of pulses. Each subsequent pulse may have a lowerpeak value and a lower bias value. FIG. 38C illustrates a correspondingaxial component of the base plasma flow in the active-zone/time space.In some embodiments, the pulses may increase the duty cycle and increasethe collision probability. The pulses shown in FIG. 38A-38C areexemplary pulses. In some embodiments, the shape of the pulse affectsthe degree of radially propagated plasma at different distances from theoutlet.

In some embodiments, for some applications, an axial component at adistal end of the plasma flow may include length of the base plasma flowbeing substantially equal to a length of the pulse plasma flow. Forthese applications, the parameters may be optimized to shape the plasmaflow in a desired way. In some embodiments, a degree of radial expansionmay be characterized by the resulting shape of plasma flow. In someembodiments, for a laminar plasma flow with a constant temperature, theratio of the average jet diameter to outlet diameter D_(J)/D_(OUT) maybe in the range of between about 2 to about 4, where D_(J) may be anaverage plasma flow diameter, with the boundary between the plasma flowand the surrounding medium considered to be an about 1,000 K isothermcontour. In some embodiments, an average flow diameter of a plasma flowwith predominant radial expansion may correspond to a D_(J)/D_(OUT)ratio of about 5 to about 10. In some embodiments, a scale of axialplasma flow expansion may be defined by a L_(J)/D_(OUT) ratio, which maybe about 50 and about 100 for laminar plasma flow, and about 15 andabout 50 for predominantly radially expanded plasma flow (e.g.,temperature threshold is about 1,000 K for 14. In some embodiments, aplasma flow length may be shorter if the temperature at the outlet orthe flow of the plasma-generating gas is lower. Thus, the plasma flowlength may be expressed as L_(j)=λD_(OUT), where λ is a coefficient thatdepends on the outlet temperature and flux λ(T, g). In some embodiments,a characteristic time of the plasma flow τ_(d) may be given by:

$\begin{matrix}{\tau_{d} = {\frac{L_{J}}{U_{J}} = \frac{\lambda D_{OUT}}{U_{J}}}} & (40)\end{matrix}$

In some embodiments, the resulting plasma flow length may define a“working distance” for a plasma-generating device. The term “workingdistance” may refer to a range of distances from an outlet of theplasma-generating device that achieves a desired effect on the surfacebeing treated. In some embodiments, the plasma flow length may depend onthe plasma flow speed, which may depend on distance due to cooling ofthe plasma flow by surrounding media such as air, and heating by thepulse plasma flow.

FIGS. 39A-39C illustrates experimental validation of the effect ofradial expansion of a plasma jet. In particular, FIGS. 39A-39C depictplasma flow generated with different conditions on tissue sample. Afterexposure of tissue sample to laminar plasma flow for a relatively shortfixed period of time, as shown in FIG. 39A, two distinguishable regionsmay be visually detected. For example, an outlet diameter of the jet maybe about 0.5 mm. A tissue crater may be formed at the intersection of aplasma jet axis and tissue surface. The depth of the crater may dependon the distance between the sample surface and nozzle of aplasma-generating device. In some embodiments, the crater may be formeddue to tissue vaporization as a result of high temperature plasma flow.In some embodiments, a vaporization rate may be directly related toplasma temperature and mass flux. Since the plasma temperature mayslowly decrease along the plasma jet axis, the depth of the crater mayalso decrease if the sample is exposed to the plasma flow for the sametime interval. In some embodiments, plasma temperature may substantiallydecrease in a direction transverse to a plasma jet direction. As aresult, areas of coagulated tissue surface may be observed next to theformed crater. For example, coagulation may be observed if local plasmaflow temperature is higher than a predetermined value (e.g., about 70°C. for an exposure time of about 1 second to about 3 seconds). Duringthis set of experiments, the tissue sample was located at differentdistances from the nozzle of the plasma-generating device. The geometriccharacteristics of the formed crater and coagulated tissue area weremonitored. Tracking of these parameters enabled estimation of a plasmajet shape.

FIG. 39A illustrates a plasma flow with oscillating outlet temperaturebetween about 6,000 K and about 14,000 K with an oscillation period ofabout 10 ms. As shown in FIG. 39A, a plasma jet length of about 50 mmand a diameter of coagulated area of 3 mm are observed. The craterobserved in the middle indicates that the plasma flow temperature andmass flux are considerably high and correspond to a high vaporizationrate of the tissue sample. This is an expected result for laminar plasmaflow. FIG. 39B illustrates experimental data for plasma flow with thesame conditions as for FIG. 39A but for an oscillation period of about35 μs. According to the theoretical model described herein forgenerating a radially expanded plasma flow, the radial expansion ofplasma jet may be observed for the corresponding frequency of outlettemperature oscillation (e.g., about 30 kHz). Indeed, as shown in FIG.39B, the diameter of a coagulated area significantly increased up toabout 20 mm, which is about 7 times larger than the observed diameterfor laminar flow with the same temperature range of outlet plasma flow.Moreover, the plasma jet length decreased as expected in this example.The observed crater in FIG. 39B indicates that still there is a smallfraction of axially propagated flow close to the nozzle. However, thedepth of the crater may be substantially lower due to a lower fractionof axially propagated plasma flow.

FIG. 39C illustrates another example of plasma flow with predominantlyradially expanded plasma flow. In this case, the outlet diameter may beabout 1.2 mm and have a similar temperature range of outlet plasma flowwith the same oscillation period of about 35 μs. The results revealformation of coagulation area of about 20 mm without forming a craterfor all distances in range from about 5 mm to about 15 mm. Therefore, anegligible or no fraction of axially propagated flow was observed forthe tested distances. The results also show that a jet diameter in theradial expansion zone may be maintained with same temperature-timeprofile when an outlet diameter increased from about 0.5 mm to about 1.2mm.

In some embodiments, an output thermodynamic parameter may include thetemperature-time profile of the plasma flow temperature at the outlet.Specifically, a thermodynamic parameter may include a temperaturerelationship between the base and the pulse plasma and the frequency ofoscillations between them. In some embodiments, a speed ratio may bedirectly related to the temperature. However, an absolute speed valuefor a predetermined plasma flow may depend on the ratio between ambientpressure and active chamber pressure, and whether the flow is choked orin a Rayleigh state. From a practical point of view, in some embodimentsfor predominantly radially expanded plasma flows, higher values ofvelocities may be more desirable. This desire may be attributed to theplasma length and the distance range of the plasma-generating device. Insome embodiments, the plasma flow length may be estimated using

$L = {{U_{T}T} = \frac{U_{T}}{f}}$

and the maximum value may be L=λ(T,g)D_(OUT). In some embodiments, themaximum plasma flow length may be limited by the absolute value ofoutlet plasma speed and outlet diameter. The maximum possible speed thatmay be achieved may be the speed of sound at a predetermined temperatureof the plasma-generating gas without an adaptive outlet nozzle. Whenworking pressure is higher than critical pressure, the outlet speed mayachieve M>1 with an adaptive outlet nozzle, where M is a Mach number.Moreover, in some embodiments, frequency relationships might also limitthe working distance. Therefore, the outlet flow may be in a chokedstate to achieve the speed M>1. Thermodynamically, this means that theflux or working pressure may be higher.

In some embodiments, predetermined ranges of thermal energy (e.g., gasmass flow) may be delivered (for a specific application) to the surfacebeing treated. In some of these embodiments, the working distance maynot be increased by increasing pulse plasma temperature. If the requiredworking distance is desired to be increased without changing theplasma-generating gas mass flow, the base plasma flow temperature mayhave low-frequency oscillation between two or more temperatures, witheach level having a corresponding temperature-time profile. An exampleof such a temperature-time profile is shown in FIG. 40 .

In FIG. 40 , the temperature oscillates between base plasma flowtemperature T_(base) and the pulse plasma flow temperature T_(pulse)temperatures with high frequency f_(HF)=1/T_(HF). The base plasma flowtemperature oscillates between T_(base) ¹ and T_(base) ², and the pulseflow temperature oscillates between T_(pulse) ¹ and T_(pulse) ² withlower frequency f_(LF)=1/T_(LF), respectively. The resulting compositetemperature-time profile includes the first temperature-time profilethat operates on (T_(base) ¹, T_(pulse) ¹) oscillations and frequencyf_(HF) and a second temperature-time profile that operates on (T_(base)², T_(pulse) ²) oscillation. The working pressure of the plasma flowgenerated as a result of this composite profile can be calculated asshown in FIG. 41 . FIG. 41 is a plot of inlet gas flow and inletpressure for boosting working pressure by oscillation of outlettemperature with two levels of amplitudes and frequencies. In someembodiments, if P_(w) ¹ and P_(w) ² are the working pressures for thefirst constituent temperature-time profile and the second constitutetemperature-time profile, the resulting inlet pressure is between P_(w)¹ and P_(w) ². In some embodiments, if a duty of low frequency pulses isD_(LF), then the inlet pressure may be obtained using the equation:

P_(w)=P_(w) ¹+D_(LF)(P_(w) ²−P_(w) ¹)   (41)

Equation (41) may be derived from equation (5). As a result of such lowfrequency pulses, the working pressure P_(W) may be higher than if itwould be for the first temperature-time profile. Similar considerationsare true for the region (T_(base) ², T_(pulse) ²), but the workingpressure P_(w) may be lower than if it would be for the secondtemperature-time profile. In some embodiments, the inlet pressure mayaffect the flow length. For a first interval 154, the plasma flow lengthmay be higher than it would have been had the first temperature-timeprofile been used by itself. The resulting composite profile may resultin the plasma flow that “superimposes” the elongated flow that wouldresult if the first temperature-time profile is used by itself andpossibly shortened flow that would result if the second temperature-timeprofile is used by itself. Moreover, since plasma flow speed may begenerated as a result of the composite, the temperature-time profile mayhave different speeds of base and pulse plasma flows compared to theplasma flows generated by the application of the first temperature-timeprofile or second temperature-time profile individually.

In some embodiments, the distribution of radial expansion along the flowaxis may be changed. Therefore, the active zone may also change comparedto the plasma flow, as compared to the flows generated as a result ofthe first and second time-temperature profiles applied individually.Overall, modulating the outlet plasma flow temperature with severalcharacteristic frequencies and amplitude levels as described herein maybe used to adjust the working pressure to a predetermined value toconfigure the shape of the plasma flow to achieve a predetermined effectfor a predetermined application.

EXAMPLES

The following examples illustrate how the shape of a plasma jet maydepend on a set of parameters. Unless specified otherwise, thetemperature-time profile in these examples may have a rectangular shapeof pulses, for example, as shown in FIG. 9 .

Example 1

Example 1 includes a gas inlet flow of about 0.5 L/min, a diameter of aheating portion of about 0.4 mm, an outlet diameter of about 0.5 mm, abase or target temperature of about 3,000 K, and a period of outlettemperature-time oscillation of about 25 μs. The duty may be set toabout 0.5 as a compromise for reasonable density and velocity ratio oftarget and initiator flows, as shown in FIG. 25 . The initiatortemperature may be equal to about 13,400 K for the same volume of targetand initiator plasma flow. The resulting plasma jet shape isschematically illustrated in FIG. 42A.

Example 2 Frequency or Period of Outlet Temperature-Time Oscillation

For the same conditions as in Example 1, but with a period of outlettemperature-time oscillation T of about 50 μs, the resulting plasma jetshape is schematically illustrated in FIG. 42B. The increase of periodleads to elongation of radially expanded plasma flow, since the plasmajet length may be estimated as L=U_(T)T, according to Eq. 19. If theperiod is substantially longer than the relationships presented in Eq.30, then laminar plasma flow may be generated.

Example 3 Volumes of Target and Initiator Plasma Flows

For the same conditions as in Example 1, but with the initiatortemperature of about 16,000 K, the resulting plasma flow may take theform illustrated in FIG. 42C. In this case, the volume of initiator flowand specific length of the initiator flow may be higher than for thetarget flow. As a result, a partial laminar flow may be formed at theend of a radially expanded part of the plasma jet as shown in FIG. 42C.

Example 4 Heating Channel Diameter

For the same conditions as in Example 1, but with a diameter of theheating channel of about 0.6 mm, the resulting plasma flow may take theform illustrated in FIG. 42D. The length of a resulting plasma jet maydecrease because the increase of a heating channel diameter maycorrespond to a working pressure drop, which in turn may result in lowervelocities that the outlet plasma flow may reach.

Example 5 Gas Inlet Flow

For the same conditions as in Example 1, but with a gas flow inlet ofabout 0.7 L/min, the resulting plasma flow may take the form illustratedin FIG. 42E. An increase of gas flow inlet may be equivalent to anincrease of working pressure, as shown in Eq. 10. The higher workingpressure may boost the outlet plasma velocity that may be reached. Thus,the plasma jet shape may enlarge with the higher values of inlet gasflow.

Example 6 Outlet Diameter

For the same conditions as in Example 1, but with outlet diameter ofabout 0.6 mm, the resulting plasma flow may take the form illustrated inFIG. 42F. In this example, higher expansion of an adaptive nozzle mayfurther increase the outlet plasma flow velocity. In some embodiments,the increase of outlet flow velocity may be achieved if the workingpressure is considerably high such that the pressure difference betweenworking and ambient pressure may be actually realized by adaptive nozzleto increase the outlet velocity. For some applications, the workingpressure may be intentionally increased to use higher expansion ofadaptive nozzle to increase the diameter of jet while keeping low outletmass flux. Such an approach may be used to achieve a highcross-sectional area of plasma flow with low power density. This may beuseful for controlling heating of a comparatively large surface area.

Example 7 Duty of the Outlet Temperature Pulses

For the same conditions as in Example 1, with a duty of about 0.4, theinitiator temperature may be about 16,000 K to meet conditions of thesame target and initiator volume of plasma flow. In this example, ahigher degree of radial expansion may be achieved and a higher fractionof target axial flow may be obtained in the first part of plasma flow asschematically shown in FIG. 42G. In case of a duty D of about 0.6 withan initiator temperature of about 11,200 K to maintain the same volumeof target and initiator plasma flow, the opposite situation is realized;the lower degree of radial expansion may be achieved, and a lowerfraction of target axial flow may be obtained, as illustrated in FIG.42H.

Example 8 Target Temperature

For the same conditions as in Example 1 with a target temperature ofabout 10,000 K, the initiator temperature may be about 21,500 K to meetconditions of the same target and initiator volume of the plasma flow.In this example, a target velocity may be higher compared to Example 1.As a result, the length and diameter of resulting plasma may beincreased, as illustrated in FIG. 421 .

Example 9 Optimization of Outlet Temperature-Time Profile

For Example 9, the inlet gas flow, diameter of heating channel, andoutlet diameter may be the same as in Example 1. The outlettemperature-time oscillation may have a profile given by the dash linein FIG. 2 , with a target temperature of about 3,000 K, maximuminitiator temperature of about 16,000 K, and effective duty of about0.6. In comparison to Example 1, the resulting plasma jet may have ahigher degree of radial expansion, and the impact of axial target flowmay have a lower fraction, as illustrated in FIG. 42J.

Parameters for Therapeutic Application

As discussed above, the duty between the pulse-initiator and base-targetplasma flow may be in a range between about 0.4 and about 0.6 togenerate predominantly radially expanded plasma flow and to achieve thesame volume of pulse and base plasma flows. Variation of pulse and basetemperatures and duty may affect the plasma flow shape as discussed inthe examples herein and shown in FIGS. 42A-42J. Control of the shape andenergy of plasma flow may be used to broaden an area of possibleapplications for the methods described herein. Some applications mightrequire a predetermined ratio between radially expanded and laminarfraction of plasma flow. For example, in a therapeutic application, aplasma-generating device may generate nitric oxide for patienttreatment. In some embodiments, a high temperature of plasma flow may beused to generate a high concentration of nitric oxide. To avoid damagedue to the high temperature, the plasma flow may be rapidly cooled downto a lower temperature (between about 30° C. and about 60° C.) that bothprotects from overheating and allows delivery of the nitric oxide beforeit decomposes in the atmosphere. In some embodiments, a method fortherapeutic application may include a high temperature (>10,000° C.)pulse-initiator plasma and low temperature base plasma flow with lowduty that may be configured for rapid cooling of the plasma flow. Forinstance, a duration of pulses may be between about 10 μs and about 25μs. The period T may be in a range of between about 50 μs and about 50ms. Thus, the duty may be substantially lower than a predetermined“optimal” range, thereby decreasing the fraction of radially expandedplasma flow. Nonetheless, the remaining small fraction of radiallyexpanded plasma flow may produce a high concentration of nitric oxide.Due to a low duty of the pulses, the resulting plasma flow may beeffectively cooled down to desired temperature for subsequent use.Moreover, the radial propagation the temperature gradient of plasma flowmay be more uniform compared to turbulent or laminar flow, thus enablinga stable condition for uniform generation of nitric oxide.

General Conditions for Generating Predominantly Radially Expanded Flow

With reference to FIG. 43 , a set of parameters for a temperature-timeprofile of outlet plasma temperature and parameters of theplasma-generating device may include a base and pulse temperatureT_(base) and T_(pulse), period T and duty D. Input plasma-generatingdevice parameters may include inlet gas flow G_(IN), outlet diameterd_(OUT), and heating channel diameter d_(H).

First, for a predetermined base temperature T_(base), the pulsetemperature may be in a range between about T_(pulse) ^(min) and aboutT_(pulse) ^(max). A lower boundary may be defined by a threshold forminimal density ratio of about 2. An upper boundary may be defined by athreshold for minimum speed of sound ratio of about 0.25:

${\frac{\rho\left( T_{base} \right)}{\rho\left( T_{pulse}^{\min} \right)} = \left. 2\Rightarrow{T_{pulse}^{\min}\left( T_{T} \right)} \right.}{\frac{a\left( T_{base} \right)}{a\left( T_{pulse}^{\max} \right)} = \left. 0.25\Rightarrow{T_{pulse}^{\max}\left( T_{base} \right)} \right.}$

FIG. 44 illustrates bottom and top boundaries of pulse temperature forpredetermined base temperatures up to about 15,000 K where argon is theplasma generating gas. An optimal pulse temperature range for argonplasma is shown in FIG. 45 . Similarly, an optimal pulse temperaturerange for air plasma is shown in FIG. 46 .

Second, in some embodiments, a period of oscillation may be less than apredetermined value T^(max), that may defined by outlet diameter andpulse temperature. FIG. 32 and Table 1 illustrate the dependence ofT^(max) on pulse temperature for a set of outlet diameters. FIG. 33illustrates a plot for a corresponding minimum frequency of outlettemperature oscillation f^(min). In some embodiments, the pulsetemperature may be in an optimal range. The T^(max) and f^(min) graphsmay be represented using the corresponding base temperature as shown inFIGS. 47 and FIG. 48 , respectively.

Third, in some embodiments, an outlet diameter may be less thanpredetermined value d_(OUT) ^(max), that may be defined by outlet pulsetemperature. FIG. 34 illustrates a dependence of d_(OUT) ^(max) on pulsetemperature. This relationship may be based on critical Reynolds numberfor minimal outlet velocities.

Fourth, in some embodiments, to avoid turbulent mode, the inlet gas flowrate may be less than critical inlet gas flow for pulse and base plasmaflows with a Reynolds number of about 2,000, as shown in Eq. 34 and 35.In some embodiments, the maximum inlet gas flow rate may be linearlyproportional to an outlet diameter. Considering the pulse temperaturemay be in an optimal range, an example of a maximum inlet gas flow rateis shown in FIG. 50 for base temperature and FIG. 51 for pulsetemperature.

Fifth, in some embodiments, mass flux in a heating channel may besufficient to provide minimal working pressure to maintain plasma flow.

$G_{IN} > {{K \cdot \frac{\pi d_{H}^{2}}{4}}\left( {D + {\sqrt{\frac{T_{P}}{T_{B}}}\left( {1 - D} \right)}} \right)}$

When the pulse temperature is in an optimal range, an example of aminimum inlet gas flow rate is shown in FIG. 52 for base temperature andFIG. 53 for pulse temperature and various diameter of heating channel.

General High Frequency (HF) Pulses for Generating Predominant RadialExpansion Plasma Flow

FIG. 54 illustrates a general outlet temperature-time profile forbase-target and pulse-initiator plasma having a set of parametersincluding base temperature level, period of pulse repetition,temperature pulse rise and fall times, temperature pulse delay falltime, and pulse temperature. For example, base temperature levelT_(BASE) may be defined for a predetermined type of action. For example,T_(BASE) may be set to a relatively low level, such as about 2,000 K andabout 4,000 K, for controlled heating of an object without vaporizationand sublimation of the treated surface boundary. T_(BASE) may be set torelatively higher level (e.g. about 9,000 K and about 11,000 K) forcontrolled speed of vaporization of the treated surface boundary. Aperiod of pulses repetition T may be between about 10 μs and about 50μs. Temperature pulse rise and fall times τ₁ and τ₂ may be between about0.01.T and about 0.1.T. Temperature pulse delay fall time τ₃ may bebetween about 0.2^(.)T and about 0.4^(.)T. Pulse temperatureT_(PULSE)=top optimal boundary of T^(PULSE) for the predeterminedT_(BASE):

$\frac{a\left( T_{base} \right)}{a\left( T_{pulse} \right)} = 0.5$

In some embodiments, pulse temperature T_(PULSE) ^(b)=bottom optimalboundary of T_(PULSE) for the predetermined T_(BASE):

$\frac{a\left( T_{base} \right)}{a\left( T_{pulse} \right)} = 0.6$

In some embodiments, pulse temperature T_(FALL)=(0.2-0.4)·(T_(PULSE)^(b)-T_(BASE)). In some embodiments, pulse temperature duration τ_(p)may define the effective duty

${D = \frac{\tau_{p}}{T}},$

which may be in a range of between about 0.4 and about 0.6. In someembodiments, a base level of temperature in the temperature-time profilemay slowly oscillate with considerably lower frequency, as shown in FIG.40 . As discussed herein, such low frequency oscillation may be used tobuild up the working pressure and tune the shape and the energy level ofa plasma jet. In some embodiments, low frequency oscillation may be inrange of between about 100 Hz and about 1 kHz.

3. Plasma-Generating System Overview

Plasma-generating devices that do not modulate required oscillations ofoutlet thermodynamic parameters may be poorly configured to generatepredominantly radially expanded plasma flows. Moreover, degradation anderosion processes associated with certain plasma-generating device mayprevent such devices from stable robust operation.

As used herein, a plasma-generating device may refer to a handpiececonfigured to generate and discharge plasma. The plasma-generatingdevice may refer collectively to the handpiece, a console unit, andconnecting wires and hoses for the transmission of energy, such aselectric current, plasma-generating gas, coolant, and other substancesand/or signals between the console unit and the handpiece. In someembodiments, the console unit may include a current control powersupply. The handpiece and current control power supply are described inmore detail herein.

FIG. 55 shows a longitudinal cross-section of one embodiment of aplasma-generating device 5500. Plasma-generating device 5500 can includecomponents that are structurally and/or functionally similar to those ofother plasma-generating devices described herein (e.g.,plasma-generating device 100, 5700, etc.). The cross-section depicted inFIG. 55 is along a longitudinal axis of the plasma-generating device5500. In operation, plasma flows from a proximal end of the generator(left side of FIG. 55 ) and may be discharged from outlet 5560 (rightside of FIG. 55 ). The flow of plasma gives meaning to the terms“upstream” and “downstream.” The discharge end of generator 5500 may bereferred to as the distal end. In general, the term “distal” refers tofacing the discharge end of the generator; the term “proximal” refers tofacing the opposite direction of distal. The terms “distal” and“proximal” may be used to describe the ends of generator 5500 as well asits elements.

The plasma-generating device 5500, as shown in FIG. 55 may comprise acathode 5506, anode 5508, and two (or more) intermediate electrodes 5510and 5512, arranged upstream of anode 5508. In some embodiments, theintermediate electrodes 5510 and 5512 and anode 5508 may be annular andform a plasma channel 5514, which extends from a position downstream ofcathode 5506 and through anode 5508. Anode 5508 may form outlet 5560,from which plasma may be discharged. Inlet 5516 of plasma channel 5514may be at its proximal end. In plasma channel 5514, plasma may be heatedand discharged through outlet 5560. Intermediate electrodes 5510 and5512 may be insulated and separated from direct contact with each otherand anode 5508 by respective annular insulator washers 5518 and 5520. Insome embodiments, plasma channel 5514 may include a heating portion 5524partially formed by intermediate electrodes 5510 and 5512 and anodeportion 5522 formed by anode 5508.

In the embodiment shown in FIG. 55 , cathode 5506 may be formed as anelongate cylindrical element. In some embodiments, cathode 5506 may bemade of tungsten, optionally with additives, such as lanthanum. Suchadditives may be used, for example, to lower the temperature that thedistal end of cathode 5506 reaches.

In some embodiments, the distal portion of cathode 5506 may have atapering end portion 5534 (e.g., tapered portion). In some embodiments,tapering portion 5534 may have a conical shape that forms a tip point5536 (e.g., distal tip) at the distal-most end of cathode 5506, as shownin FIG. 55 . In some embodiments, cathode 5534 may be a truncated cone.In other embodiments, cathode tip 5534 may have other shapes (e.g.,tapering toward anode 5508). In some embodiments, plasma-generatingdevice 5500 may further comprise a plastic water divider 5550 thattogether with outside surfaces of intermediate electrodes 5510 and 5512,anode 5508, and outside surfaces of insulators 5518 and 5520, and aninside surface of the outer sleeve 5566 connected to anode 5508 form acooling channel. Even though outer sleeve 5566 may be integrallyconnected to the anode, the portion of the integral structure to whichpositive electrical charge may be applied and concentrated may beconsidered to be anode 5508. The remaining outer portion may not carryelectric charge and may be considered a passive outer sleeve 5566.

In some embodiments, a first intermediate electrode 5510 may define aplasma chamber 5560 that connects to an inlet 5516 of plasma channel5514. In some embodiments, plasma chamber 5560 may have a cylindricalportion 5562 and, in some embodiments, may optionally have atransitional portion 5564 that connects the cylindrical portion 5562 toa plasma channel inlet 5516. In some embodiments, a cross-sectional areaof cylindrical portion 5562 may be greater than a cross-sectional areaof plasma channel inlet 5516.

FIG. 55 also depicts an insulator sleeve 5554 extending along and arounda portion of cathode 5534. In some embodiments, cathode 5506 may bearranged substantially in the center of the through hole of insulatorsleeve 5554. In some embodiments, an inner diameter of insulator sleeve5554 may be greater than the outer diameter of cathode 5506. Thedifference in these diameters may result in a gap formed by the outersurface of cathode 5506 and the inner surface of insulator sleeve 5554.In some embodiments, insulator sleeve 5554 may be made of atemperature-resistant material, such as ceramic, temperature-resistantplastic, combinations thereof, and the like. In some embodiments,insulator sleeve 5554 may be configured to protect constituent elementsof plasma-generating device 5500 from heat generated by cathode 5506,and in particular by cathode tip 5534 during operation. In someembodiments, insulator sleeve 5554 and cathode 5506 may be arrangedrelative to each other so that the distal end of cathode 5506 projectsbeyond the distal end 5556 of insulator sleeve 5554.

In some embodiments, cathode chamber 5560, as shown in FIG. 55 , mayhave a circular cross-section. In some embodiments, cathode chamber 5560and plasma channel 5514 may be arranged substantially concentrically toeach other. In some embodiments, cathode 5506 may be arrangedsubstantially concentrically with plasma chamber 5560. In someembodiments, cathode 5506 may extend into plasma chamber 5560.

In some embodiments, the proximal end of cathode 5506 may be connectedto an electrical conductor connected to a power supply. In someembodiments, anode 5508 may be connected to the power supply. In someembodiments, a gas flow controller (not shown in FIG. 55 ) may beconnected to the plasma-generating device. During operation, theplasma-generating gas may flow from a gas controller (e.g., controller102 depicted in FIG. 1 ) through an expansion chamber (e.g., expansionchamber 104 depicted in FIG. 1 ) and into the gap formed by the outsidesurface of cathode 5506 and the inside surface of insulator sleeve 5554.In some embodiments, the plasma-generating gas may flow along cathode5506 inside insulator sleeve 5554 toward anode 5508. (As mentionedabove, this direction of the plasma flow gives meaning to the terms“upstream” and “downstream” as used herein.) As the plasma-generatinggas passes distal end 5556 of insulator sleeve 5554, the gas may enterinto cathode chamber 5560. The plasma generating gas may be heated bythe electric arc formed between cathode 5506 and anode 5508. Thisheating of the passing plasma-generating gas may result in the formationof a plasma flow discharged from outlet 5560. By controlling the currentapplied between cathode 5506 and anode 5508 and the plasma-generatinggas flow rate, the desired temperature-time profile may be created atoutlet 5560 of generator 5500.

FIG. 57 depicts an alternative embodiment of a plasma-generating device5700. Plasma-generating device 5700 can include components that arestructurally and/or functionally similar to those of otherplasma-generating devices described herein (e.g., plasma-generatingdevice 100, 5500). In some embodiments, plasma-generating device 5700may include an isolator 5710 having a complex shape as shown in FIG. 57. In some embodiments, the isolator 5710 may have a shape similar to theinner walls of insulator sleeve 5554, cathode chamber or plasma chamber5560, and plasma channel 5514. In some embodiments, the isolator 5710may be made of high temperature resistant material with high heatconductivity. In some embodiments, the isolator 5710 may be made ofaluminum nitride ceramics that may have a thermal conductivity of about280 W/(m·K). For comparison, a thermal conductivity of copper alloysused for intermediate electrodes in some embodiments may be in range ofbetween about 350 W/(m·K) and about 400 W/(m·K). In some embodiments,the isolator 5710 may take the place of the insulator sleeve 5554, firstintermediate electrode 5510, other intermediate electrodes 5512, andseparators 5518 and 5520. In some embodiments, the heat conductivity ofisolator 5710 may need to be relatively high to avoid overheating.Similar to device 5500, a water divider 5750 together with outsidesurfaces of isolator 5710 and inside surface of an outer sleeve 5706connected to anode 5708 may form a cooling channel, in some embodiments.

In some embodiments, a plasma-generating device may include a cathodeincluding a tapered distal portion, and an anode disposed downstreamfrom the cathode and being electrically insulated from the cathode. Insome embodiments, the anode may define an opening therethrough. In someembodiments, a plurality of intermediate electrodes may be disposedbetween the cathode and the anode. The plurality of intermediateelectrodes may be electrically insulated from each other and from theanode and the cathode. In some embodiments, each intermediate electrodefrom the plurality of intermediate electrodes may define an openingtherethrough such that the openings in the plurality of intermediateelectrodes and the anode collectively define a plasma channel fordischarging a plasma flow. In some embodiments, the plasma channel mayinclude a first portion having a first cross-sectional diameter, and asecond portion having a second cross-sectional diameter. In someembodiments, the first cross-sectional diameter may be at least fourtimes the second cross-sectional diameter. In some embodiments, aninsulator sleeve may extend along a surrounding a portion of thecathode.

In some embodiments, a distance from a distal end of the cathode to thesecond portion of the plasma channel may be at least 1.5 times thesecond cross-sectional diameter. In some embodiments, the opening in theanode has a cross-sectional diameter at a proximal end of the anode thatmay be less than a cross-sectional diameter at a distal end of theanode. In some embodiments, an outer sleeve may be coupled to the anode,and a divider may be disposed between the outer sleeve and the pluralityof intermediate electrodes, the divider with outside surfaces of theplurality of intermediate electrode, an outside surface of the anode,and an inside surface of the outer sleeve collectively defining acooling channel for cooling the plasma channel.

In some embodiments, the cathode may be disposed in a cathode chamberhaving a diameter dcc. In some embodiments, the diameter dcc may be atleast four times the second cross-sectional diameter. In someembodiments, a distance between a distal end of the insulator sleeve anda distal end of the cathode is at least a diameter of the cathode andless than 1.6 times the diameter of the cathode. In some embodiments, alength of the anode may be between two times to eight times a diameterof the anode.

Heating Channel and Anode Channel

In some embodiments, the plasma-generating device as shown in FIG. 55may comprise a cathode assembly which may include a cathode holder,ceramic insulator and tungsten cathode affixed in a cathode holder, ananode, and two or more intermediate electrodes. The anode and theintermediate electrodes may form a plasma channel. The firstintermediate electrode that may be closest to the cathode may also forma cathode chamber around the cathode ends. The plasma channel maycomprise three channels including a cathode chamber, a heating channel5524, and an expansion portion of an anode channel. The diameter of theexpansion portion may increase toward the anode end.

In some embodiments, heating portion 5524 may be formed by two or moreintermediate electrodes. In some embodiments, heating portion 5524 maybe formed by a single intermediate electrode or by six or moreintermediate electrodes.

In some embodiments, heating channel 5524 may be configured to heat theplasma-generating gas to a predetermined (e.g., relatively high)temperature to provide a predetermined temperature profile of outletplasma. For the fixed current going between cathode and anode, thesmaller diameter of heating channel 5525, d_(H), may correspond to arelatively higher arc temperature and hence a relatively highertemperature of outlet plasma. Therefore, a predetermined relationshipbetween current and diameter of heating channel may be maintained togenerate plasma.

In some embodiments, oscillating outlet plasma temperature may beconfigured to generate predominantly radially expanded andvolumetrically oscillating plasma flows. In terms of plasma-generatingdevice 5500, the current may be configured to oscillate to providepredetermined outlet plasma conditions. In some embodiments, the appliedoscillating current may be characterized by RMS current. The term RMScurrent may refer to alternating current calculated as a root meansquare.

In some embodiments, if plasma-generating device 5500 is subject to sizeconstraints, such as for key hole surgeries, a max RMS current may belimited to between about 12 A and about 15 A. This relationship arisesfrom a cross-section restriction for current conductive elements of thegenerator and heat dissipation from a plasma channel to cooling water.In some embodiments, operation of a plasma-generating device with asmall cross-sectional area at higher RMS current may not be practicaldue to high current density that correspond to high amount of generatedheat that cannot be efficiently dissipated by a cooling system having asmall diameter. The total RMS current may affect heat losses to an anodechannel. For example, for argon plasma anode losses, Q_(A) may beQ_(A)=10* IRMS (W), where I_(RMS) is RMS current.

For the sake of simplicity, the following heating channel relationshipsmay be based on a surgical application embodiment, which may imply apredetermined size of a plasma-generating device and RMS currentrestriction. In some embodiments, a predetermined temperature range andprofile of outlet plasma flow may be defined by both RMS current and adiameter of a heating channel. This means that for plasma-generatingdevices having a larger cross-sectional area, an appropriate scaling ofthe parameters may be applied to meet the same relationship.

In some embodiments, to generate volumetrically oscillated plasma flowwith controlled axial and predominant radial expansion, the structure ofRMS current IRms may include a predetermined range of relatively lowfrequency current with amplitudes of between about 2 A and about 30 Awith a period of oscillation TLF between about 5 ms and about 50 ms, anda duty D of between about 0.05 and about 0.6, and a relatively highfrequency current with amplitudes of between about 5 A and about 30 Awith a period of oscillation T_(HF) of between about 10 μs and about 50μs and a duty D of between about 0.25 and about 0.75. In someembodiments, a max RMS current may not directly limit the maximumcurrent rather than relationship between relatively high and low currentduration. For example, the structure of current may include a smallfraction of high current with an amplitude of about 30 A while an RMScurrent may still be lower than about 12 A.

In some embodiments, a diameter of a heating channel may be determinedbased on a predetermined temperature range of outlet plasma. In someembodiments, a plasma-generating system may be configured to generateoutlet plasma with various extent of radial and axial components.Therefore, the diameter and length of a heating channel may be adjustedto provide plasma with temperature in range of between about 2,000 K andabout 25,000 K. In some embodiments, heating of the inlet roomtemperature gas may occur due to energy transfer from arc electrons toheavy particles of the plasma-generating gas. In some embodiments, theheat may radially dissipate towards the heating channel walls that maybe cooled by water. The corresponding energy balance for propagatedplasma-generating gas may be given by:

$\begin{matrix}{{{\rho\upsilon c_{p}\frac{dT}{dz}} + {\frac{1}{r}\frac{d}{dr}\left( {\lambda r\frac{dT}{dr}} \right)}} = {\frac{3}{2}\delta{vn}_{e}{k\left( {T_{e} - T} \right)}}} & (42)\end{matrix}$

where T is gas temperature, z and r are axial and radial variables, ρ isgas density, v is gas flow velocity, c_(p) is specific heat capacity, λis gas thermal conductivity, T_(e) and n_(e) are electron temperatureand concentration, v is collision frequency, and k is the Boltzmannconstant.

In some embodiments, an arc electron temperature may be defined byheating with conducted power density P=jE and cooling by gas and wallsof a heating channel. The relationship between electron temperature, arccurrent, and diameter of a heating channel may be comparatively complexand in many cases may be estimated based on empirical dependencies. Insome embodiments, an average electron temperature T_(e) may beproportional to the ratio of arc current to the diameter of heatingchannel I/d_(h). More precise dependencies may use a combination ofratio I/dh and heating channel diameter I/d_(h) ² for a predeterminedrange of diameters d_(h) and currents.

It should be noted that in Eq. 42 and other estimations, energy lossesdue to radiation are not considered. However, their contribution mightshift the resulting temperature plateau values or slightly affect theheating rate. The comparison of calculated values with experimentaldata, involving measurements for heating channel of various diameters ina range of between about 0.4 mm and about 1.2 mm shows a reasonableapproximation for the purposes described herein.

FIG. 59 demonstrates the experimental (shown in FIG. 59 as points) andtheoretical (shown in FIG. 59 as lines) distribution of average plasmatemperature along an axis of a heating channel for the fixed mass flowand diameter of the heating channel and constant current in the range ofbetween about 3 A and about 12 A. As shown, the gas may be graduallyheated until it reaches a plateau where the generated heat due to thecollisions with electrons may proportionally dissipate by radiation andradial heat diffusion to cool the walls of the heating channel. In someembodiments, the relatively higher current may correspond to arelatively higher temperature of electric arc and hence to highertemperature of electrons T_(e). In some embodiments, electrontemperature may define the initial heating rate and the temperature ofthe plateau. For relatively low values of current, an initial heatingrate may be considerably lower and the temperature may not reach theplateau within the first 4 mm. These results show that at a relativelyhigher current, the gas may be heated to a maximum temperature within ashort distance while longer distances may be required for relativelylower current. This effect may be beneficial since a sufficiently shortheating channel may be used to obtain a predetermined (e.g., high, low)plasma outlet temperature.

FIGS. 60 and 61 illustrate a calculated average temperature distributionfor various diameters of a heating channel in a range of between about0.2 mm and about 1 mm, with a constant current of between about 20 A andabout 4 A, respectively. In some embodiments, diameters of heatingchannels d₁-d₇ corresponds to about 0.2 mm, about 0.3 mm, about 0.4 mm,about 0.5 mm, about 0.6 mm, about 0.8 mm, and about 1.0 mm,respectively. In some embodiments, the effect of diameter at relativelyhigh current shows that the highest temperature plateau may be reachedfor a diameter of about 0.4 mm. The larger diameter may result in arelatively low maximum outlet plasma flow temperature due to relativelylow electron temperature T_(e). The smaller diameter, however, mayresult in a decreased maximum outlet plasma flow temperature. This maybe due to higher heat losses to a cooling system that may be affected byhigh radial temperature gradient for small diameters of heating channel.As shown in FIG. 61 , at a relatively low current, the plasmatemperature may gradually increase along the axis and a smaller diametermay generally correspond to higher temperatures. At a relatively lowcurrent, it takes a higher distance to reach the plateau. Moreover, fora heating channel of between about 0.2 mm and about 0.3 mm, the maximumtemperature may be higher than for a heating channel diameter of about0.4 mm in contrast to the observed dependence for relatively highcurrent. In comparison to relatively high current, the observeddifference for relatively low current may be mainly due to lowerelectron temperature at the low current, and hence a lower temperaturegradient that may result in lower heat losses at a smaller diameter of aheating channel. For relatively high currents, the observed diameterthat corresponds to the maximum temperature of the plateau mightslightly shift due to a higher temperature gradient. However, for apredetermined range of temperature, this effect may not be substantial.

In some embodiments, a plasma-generating device may be configured togenerate predominantly radially expanded and volumetrically oscillatingplasma flows for surgical application utilizing pulse currents ofvarious levels, such as at about 15 A, about 20 A, and about 30 A toachieve various degree of radial expansion for adjusting the appliedenergy to the tissue. Experiments show that a diameter of heatingchannel may be about 0.4 mm. This relationship was found to be optimalfor some embodiments to achieve a high range of outlet plasmatemperature and show competitive performance for various regimes ofoutlet temperature oscillation.

The demonstrated calculation of average plasma temperature (FIGS. 59,60, 61 ) along the axis of heating channel may correspond to gas flowsfor surgical application, which may be between about 0.2l/min and about0.6l/min. In some embodiments, the range may be related to energy thatmay be required to achieve various effects on tissue during thetreatment with the plasma-generating device. In some embodiments, thelength of the entire heating channel may depend on the flow rate of theplasma generating gas. In some embodiments, a longer heating channel maybe required to heat plasma generating gas with a greater flow rate. Insome embodiments, for a predetermined range of gas flow, a length of theheating channel may be about 1 mm.

In some embodiments, the length of each intermediate electrode formingheating channel 84, l_(ie), may depend on a diameter of heating channeld_(o) and may be in the range of between about one time to two times adiameter of d_(h). In some embodiments, a flow rate of plasma generatinggas may have a heating channel formed by at least two intermediateelectrodes. In some embodiments, the length of the entire heatingchannel l_(h) may be approximated by multiplying the number ofintermediate electrodes that form the heating channel by the length ofsuch an intermediate electrode l_(ie).

In some embodiments, electrons of an electric arc may be transferred toan anode surface while generated plasma propagates towards an anodeoutlet. In some embodiments, an anode channel design may be configuredto level the static pressure of outlet plasma flow to about the ambientpressure. This may be achieved using, for example, adaptive nozzledesign, where the diameter of an anode nozzle may be configured toexpand towards the outlet such that the plasma flow may uniformly expandto the new diameter. In some embodiments, leveling the static pressureof outlet plasma with ambient pressure may be useful for surgicalapplications where excess static pressure may increase the risk of gasembolism or blood vessel blockage caused by gas penetration in the bloodvessels.

As previously discussed, the plasma flow may be generally choked at theexpansion section of the channel where plasma flow propagates. In someembodiments, the choked condition may occur in the anode channel wherethe gas flow expands. Anode channel expansion may occur in various waysbased on an application of the plasma-generating device. In someembodiments, a relationship for the anode channel may be that the ratioof outlet cross-sectional area to an inner cross-sectional area of aheating channel may be adjusted to reduce the static pressure of outletplasma at least relative to ambient pressure. For example, an adaptivenozzle design may be used.

In some embodiments, an outlet diameter dour of the anode may becalculated using Eq. 16. For example, for a heating channel of about 0.4mm, a working pressure of about 5 bars and an outlet temperature ofabout 5,000 K and an outlet diameter of about 0.45 mm may be used toavoid excessive static pressure of plasma flow and increase the velocityabout 1.6 times. In some embodiments, higher value of outlet diameters,such as about 0.5 mm, may be used in some applications, such as surgicalprocedures, to protect against excessive static pressure. It should benoted that adaptive nozzle design may involve a predeterminedhydrodynamical shape (e.g., de Laval nozzle) of the channel tofacilitate the uniform expansion of plasma flow and avoid excessivefriction at the anode surface. In some embodiments, excessive frictionmay induce small perturbation in plasma flow that may result in ashorter length of a plasma jet.

For a therapeutic application such as an antimicrobial treatment oftissue due to release of nitric oxide during operation ofplasma-generating device, a larger diameter of a plasma jet may bebeneficial since it expands the area of treatment, thereby making thetreatment easier for an operator and taking less time to perform. Insome embodiments, an expansion of plasma flow may be achieved in theanode channel. In some embodiments, a gas flow rate may be comparativelyhigher to increase the working pressure in the cathode chamber and allowhigher expansion of plasma flow in the anode channel by adaptive nozzledesign with a larger outlet diameter. Moreover, the higher expansion ofthe anode channel may increase the plasma flow velocity. This may beuseful to achieve better conditions for radial expansion of plasma flow.

For an application that requires relatively high gas flow, the optimallength of a heating channel may be longer than for previously discussedsurgical applications. FIG. 62 shows the calculated average temperaturedistribution for various gas flows in a range of between about 0.4 l/minand about 1.4 l/min at constant current of about 20 A. In someembodiments, gas flows G₁-G₅ corresponds to about 0.4l/min, about0.8l/min, about 1.0l/min, about 1.2l/min, and about 1.4l/min,respectively. As shown in FIG. 62 , the length of a heating channel maybe adjusted for relatively higher gas flows. For example, a suitablelength of the heating channel may be between about 3 mm and about 4 mmfor a gas flow of about 1.4l/min.

In some embodiments, heating channel relationships may be based on asize constraint and energy demands of a predetermined application (e.g.,medical procedure). For other applications, a geometric relationship maybe scaled to maintain the ratio of applied RMS current to a diameter ofheating channel of a plasma-generating device. Maintaining this ratiomay generate similar electron temperatures in the electric arc and asimilar range of plasma temperatures. In some embodiments, the gas flowrate may define the applied energy range to the treated object. Forexample, to meet the relationships for the length of heating channel,the mass flux in the heating portion may be maintained.

Cathode Chamber

In some embodiments, plasma-generating devices that operate withoscillating current that generate predominantly radially expanded and/orvolumetrically oscillating plasma flows may have more stringentrequirements compared to other continuous plasma-generating devices.Oscillating current involves additional dynamic processes in acathode-anode system related to erosion and stable plasma generation.Accordingly, certain plasma-generating devices may fail (e.g., degrade)if they operate with oscillating current and the high frequencydescribed herein.

Cathode-anode failure in the presence of current oscillation with highor low frequencies has been experimentally analyzed to establishparameter ranges for the plasma-generating devices described herein. Theexperimental setup focused on minimizing degradation and prolonging thelifetime of the plasma-generating device for a wide range of operatingconditions including the shapes of current-time profiles andcharacteristic frequencies of oscillation. Geometric relationships ofvarious component dimensions were obtained. In some embodiments, theserelationships may be satisfied for a sufficiently stable and robustoperation.

In some embodiments, a performance test may include 3 regimes (lastingfor about 20 minutes each) of arc current oscillation with low frequency(LF) and high frequency (HF) pulses. FIG. 63A illustrates LF pulses withRMS current of 0.3·I_(RMS) ^(max) and HF pulses with RMS current of0.7·I_(RMS) ^(max). FIG. 63B illustrates LF pulses with RMS current of0.4·I_(RMS) ^(max) and HF pulses with RMS current of 0.6·I_(RMS) ^(max).FIG. 63C illustrates LF pulses with RMS current of 0.5·I_(RMS) ^(madx)and HF pulses with RMS current of 0.5·I_(RMS) ^(max)·I_(RMS) ^(max) is amaximum RMS current for the plasma-generating device. Such experimentalsetup may be chosen to ensure stable and reliable generation of plasmawithin various conditions.

Voltage and current between various parts of a plasma-generating device(e.g., plasma-generating device 100, 5500, 5700) were measured toinvestigate possible negative factors. FIG. 58 schematically illustratesthe connection locations and corresponding designation for voltages,namely U_(C-E1) for cathode chamber, U_(E1-E2) for heating channel, andU_(E2-A) for anode channel. For some experiments, a total voltagebetween cathode and anode U_(C-A), or a voltage between a firstelectrode (e.g., first electrode 5510) and anode U_(E1-A) was monitored.

With reference to FIG. 56 , the geometric relationships between thecomponents of the plasma-generating device 5500 were varied, and foreach combination of parameters, performance tests were carried out. Thestrongest effect on degradation of plasma-generating device was foundwhen the diameter of cathode chamber 5560 and specifically itscylindrical portion 5562 (e.g., d_(cc)), was varied in relation to thediameter of heating channel 124 (e.g., d_(h)). FIG. 64 shows lifespanacceptance criteria P may depend on a ratio d_(cc)/d_(h). Thisacceptance criteria was calculated as a ratio of operation time that theplasma-generating device worked before it failed to the total time ofthe performance test, which may be about 60 minutes in some embodiments.If P=1, than the generator could operate for at least 60 minutes.

In some embodiments, the variation of other parameters ofplasma-generating device 100 were shown (based on the performance tests)to be less critical than the variation of a diameter of cylindricalportion 5562 of cathode chamber 5560.

In some embodiments, the distance between a cathode tip end point 5536and the heating channel inlet 5516 (e.g., I_(TH), tip to heat channeldistance), may be at least about 1.5 times larger than the diameter ofheating channel 5524 (e.g., d_(h)). In other words, the cathode tip endpoint position may be at a predetermined distance from a proximal end ofthe heating channel to avoid the influence of the heating channel. Ifthe heating channel is too close to a cathode tip, it may effectively“reduce” the diameter of cathode chamber 5560. As discussed above, insome embodiments, a small diameter of the cathode chamber may have anegative effect on device lifespan. For the same reason, the cathode tipend point 5536 may not be inside the insulator sleeve 5554 in someembodiments, and the protruding distance between distal edge 5556 ofinsulator sleeve and cathode tip end point 5536 (e.g., I_(p)) may be atleast equal to the cathode diameter (i.e., diameter of the cylindricalpart of cathode 5506) (e.g., dr).

In some embodiments, a sufficiently short protruding distance I_(p) maybe configured to efficiently cool the cathode by incoming gas. In someembodiments, the ratio of protruding distance to cathode diameter d_(c)may be at most about 1.6. Furthermore, to ensure reliable cooling of thecathode 5506, a ratio of the inside diameter of insulator sleeve 5554(e.g., d_(INS)), and cathode diameter d_(c) may be in the range ofbetween about 0.7 and about 0.85.

Table 2 summarize the results of performance testing and indicatessuitable ranges and optimal parameters of a plasma-generating device.

TABLE 2 Tested and acceptable range and parameters of plasma-generatingdevices Suitable Parameter Acceptable operation Parameter designationTested range operation range values Heating channel d_(H) (0.2-1.0) mm(0.4-1.0) mm 0.4 mm diameter, mm Heating channel l_(H) (1.5-6.0) · d_(H)   (2-5) · d_(H) 3 · d_(H) length, mm Cathode diameter, d_(C) (0.5-1.0)mm (0.5-1.0) mm 0.5 mm mm Cathode tip length, l_(tip) (1.0-2.5) · d_(C)(1.5-2.0) · d_(C) 1.9 d_(C) mm Cathode chamber d_(CC) (1.0-5.0) · d_(H)≥4.0 d_(H) 1.8 mm diameter, mm Tip-to-heating l_(TH) (0.5-3.0) · d_(H) ≥1.25 · d_(H) 0.7 mm channel distance, mm Cathode tip l_(P)  (0-20) ·d_(C) (1.0-1.6) · d_(C) 1.4 mm protrusion, mm Cathode chamber l_(CC)l_(TH) + l_(P) l_(TH) + l_(P) 2.1 mm length, mm Inner insulator d_(INS)(1.1-2.5) · d_(C) (1.1-1.4) · d_(C) 1.2 mm diameter, mm Anode diameter,mm d_(A) (0.4-2.0) mm (0.4-2.0) mm 0.5 mm Anode length, mm l_(A)(2.0-8.0) · d_(A) (2.0-4.0) · d_(A) 2 mm

The performance tests described herein facilitate the design ofplasma-generating devices configured to operate with oscillating arccurrent that avoid rapid degradation of the cathode-anode system. Thefollowing discussion includes analysis of dynamic processes in thecathode-anode system and erosion mechanisms in plasma-generating devicesthat reduce detrimental effects.

In some embodiments, the generation of thermal plasma may begin with acold cathode and include operating phases such as spark, glow, and arcdischarge. In a first phase (e.g., spark), an electric spark may begenerated between a cathode and an anode using a relatively highelectric field and voltage. Then, the accelerated electrons of the sparkmay interact with plasma-generating gas in a glow phase (e.g., secondphase) to form positively charged ions, which in turn may bombard thecathode. The glow phase may be maintained by relatively high voltage andrelatively low currents. As the current increases, a part of the cathodemay be sufficiently heated by bombardment of returning ions to inducethermal emission of electrons from cathode. Next, in an arc dischargephase (e.g., third phase), the emitted electrons may reach apredetermined number large enough such that the arc current between thecathode and the anode may be maintained by a relatively low voltage. Thecurrent density in the third phase may be substantially larger comparedto a first and second phase. In some embodiments, the high current maybe necessary to heat the gas to a high temperature.

In some embodiments, when a plasma-generating device uses a constantcurrent, a stationary cathode potential may be established. A totalelectric arc current through the cathode may include negatively chargedemitted electrons, positively charged bombarding ions, and returnedback-diffused electron currents.

I(t)=I_(ee)+I_(i)−I_(bde)   (43)

where I_(ee), I_(i), and I_(bde) are total or integrated current ofemitted electrons, bombarding ions, and returned electrons over cathodesurface, respectively.

In some embodiments, these currents may be directly related to energybalance of the cathode surface. In some embodiments, the heatingmechanism of the cathode and the incoming heat flux to the cathodesurface may include bombarding the returning ions Q_(i), andback-diffusing plasma electrons Q_(bde). In some embodiments, thecooling mechanism and outgoing heat flux may include thermal emission ofcathode electrons Q_(ee) and dissipated energy Q by conduction throughthe cathode body and by vaporization of the cathode material at hightemperatures.

Q_(i)+Q_(bde)=Q_(ee)+Q   (44)

For steady-state operation, when the cathode and plasma temperatures donot change, the energy balance of the cathode surface may be given asfollows:

$\begin{matrix}{Q = {{I_{i}\left( {{\frac{5}{2}\frac{{kT}_{h}}{e}} + U_{c} + A_{i} - A_{f}} \right)} + {I_{bde}\left( {{\frac{5}{2}\frac{{kT}_{e}}{e}} + A_{f}} \right)} - {I_{ee}\left( {{2\frac{{kT}_{s}}{e}} + A_{f}} \right)}}} & (45)\end{matrix}$

where T_(h), T_(e) are respectively ion and electron temperature inproximity of cathode surface, and T_(s) is cathode surface temperature.U_(c) may be cathode potential drop in the sheath, A_(i), A_(f) arerespectively gas ionization energy and work function of cathodematerial.

In some embodiments, characteristic times of the processes involved inthe energy balance may vary. For example, a characteristic time for heatdiffusion through plasma with a characteristic length of 1 mm may be ina range of between about 10 ms and about 50 ms. For plasma-generatingdevices operating with relatively high frequency, an arc currentrate-of-rise and rate-of-fall may be in a range of between about 5 A/μsand about 10 A/μs for a leading edge of a current pulse and betweenabout 10 A/μs and about 30 A/μs for a trailing edge of a current pulse.For these conditions, the characteristic time of arc current developmentmay be in a range of between about 0.5 is and about 1 μs.

In some embodiments, characteristic times that relate to the processesof plasma state establishment may include the parameters of current andenergy balance. In some embodiments, the terms “plasma development time”and “plasma recombination time” may be used to estimate time toestablish ion concentration and plasma temperature radial distributioncorresponding to steady-state operation with constant current. In someembodiments, a plasma development time may refer to when arc currentdemand increases and ion concentration and plasma temperature aretemporally lower than corresponding values in steady-state operation. Insome embodiments, a plasma recombination time may refer to when arccurrent is decreased and excess ion concentration and plasma heatdissipates until it reaches values that correspond to a new steady-stateoperation with lower arc current. In some embodiments, plasmadevelopment and recombination time may refer to a plasma state in thecathode-anode channels and are different from adevelopment/recombination time of plasma jet that refers to outletplasma jet characteristics.

In some embodiments, plasma recombination time may be defined by a heatdiffusion mechanism and, as described above, may be significantly lowerthan a characteristic time of arc current change. In some embodiments,for cylindrical channels, the faster diffusion rate may be achieved forsmaller diameter of channel and lower wall temperature.

In some embodiments, the described characteristic times may define howfast the corresponding parameters such as arc current and ion currentmay be changed. In some embodiments, the ion current and correspondingheat flux due to returned ions may depend on ion concentration in theproximity of a cathode surface. Accordingly, heating fraction by ionbombardment may be defined by plasma state and may not immediatelyrespond to the arc current change due to the difference incharacteristic times.

The equations (43) and (45) describe equilibrium of established currentsand energy balance for steady-state operation at constant arc current.In some embodiments, when equilibrium is reached, the difference incharacteristic times may not affect the plasma-generating device.However, in case of non-steady-state operation, a difference incharacteristic times may shift the current and energy balance. The shiftin current balance may result in a higher fraction of ion current that,in turn, may increase the energy fraction that needs to be dissipated bycathode body. In some embodiments, rapid changes of arc current maycorrespond to an even higher shift in balance. In case of operation withoscillating current, the energy balance may be significantly shifted,and accumulated excess of heat energy may result in overheating of thecathode. The following experiments were carried out to analyze theinfluence of this effect for oscillating arc current.

In some embodiments, a rapid degradation of an cathode-anode system wasobserved for operation with oscillating current at high frequencies. Insome embodiments, the term “cathode chamber potential drop” may refer tothe voltage measured between cathode 5506 and first intermediateelectrode 5510. In some embodiments, the term “heating channel potentialdrop” may refer to the voltage measured between first intermediateelectrode 5510 and anode 5508. FIGS. 65A and 65B show volt-amperecharacteristics for oscillating arc current with relatively high (solidlines) and relatively low frequency (dash lines). The measured voltagein FIG. 65A corresponds to cathode chamber potential drop U_(C-E1), andin FIG. 65B corresponds to heating and anode channel potential dropU_(E1-A). The relatively high frequency results in distortion of thecharacteristics in comparison to low frequency. To investigate thefactors corresponding to the observed voltage, distortion voltage wasmeasured for cathode chamber U_(C-E1), heating channel U_(E1-E2), andanode channel U_(E2-A), as shown in FIG. 58 . The observed voltagedistortion mainly occurs for cathode chamber potential drop U_(C-E1). Nosignificant difference between high and low frequency may be found forheating channel or anode channel as may be seen in FIG. 65B. Thus, themajor contributor to this effect may be near-cathode processes. Theobserved distortion in volt-ampere characteristics indicates that athigh frequencies, the difference in characteristic times of cathodeprocesses play a role in current and energy balance.

FIG. 66B shows a schematic of a typical time scan of cathode chamberpotential drop U_(C-E1) for oscillating current with relatively lowfrequency 160 and relatively high frequency 162. The correspondingcurrent oscillates between I₁ and I₂ (FIG. 66A). The actual period ofoscillation T may be substantially longer for low frequency 160 than forhigh frequency 162. The current change rate (I₂-I₁)/Δτ_(I) may be muchhigher for high frequency 162. In case of a slowly changed current andlow frequency 160, the voltage may be oscillating between U₁ and U₂,which relates to stationary values for constant current I₁ and I₂,respectively. In some embodiments, if the frequency of oscillation isincreased, the current change rate may be increased to maintain theshape of a current profile. In some embodiments, if the frequency issufficiently high, the resulting shape of a voltage time scan maycorrespond to high frequency 162.

In some embodiments, when the current is rapidly raised from I₁ to I₂,at the point 166 (FIG. 66B) the voltage may go higher than stationaryvalue U₂, which refers to established voltage at constant current I₂. Insome embodiments, the higher voltage may be necessary to developconditions for new energy and current balance, corresponding to currentI₂. In some embodiments, an accelerated increase of emitted electronsmay occur, and hence an increase of ion concentration near the cathodeand an increase of cathode temperature due to higher number of returnedions and finally cathode heat balance. In FIG. 66B, the voltage reachesits peak at the point 166, and then it decreases towards stationaryvalue U₂, but before reaching U₂ at the point 168, the current demandmay rapidly decrease. In some embodiments, at the point 170, the ionconcentration in the surrounding plasma may be substantially larger thanthe corresponding concentration for steady-state operation at currentI₁. In some embodiments, before oversaturated plasma recombines to levelof current I₁, the fraction of ion current may be much higher comparedto stationary one. As a result, the cathode chamber potential drop mayreach very low values close to zero, and then recover towards astationary value U₁.

Experiments have been conducted to verify the influence of plasma stateon current and energy balance. FIGS. 67A-67B demonstrate time scans ofarc current and cathode chamber potential drop U_(C-E1) for oscillatingcurrent with fixed shape of current pulses but different interval τ_(i)between pulses. With reference to FIGS. 67A-67B, at the end of a currentpulse at the point 172, the cathode chamber potential drop may reachalmost the same value. At this moment, the ion concentration in theproximity of cathode surface may be considered the same for τ_(i) of 10and 30 μs (FIGS. 67A-67B). In some embodiments, when the arc current isreduced to a base value, the cathode chamber potential drop U_(C-E1) mayreach a minimum value at point 174, and then may rise until point 176when a new pulse may be started. As discussed herein, the observedminimum may be explained by a higher fraction of ion current in thecurrent balance. As the excess of ion concentration recombines, thecathode chamber potential drop U_(C-E1) may increase and for asufficiently long interval duration τ_(i) to reach value U₁ 180. In someembodiments, if the interval duration τ_(i) is shorter than the time ofplasma recombination, then the cathode chamber potential drop U_(C-E1)may not reach value U₁ at point 176 (FIG. 67A). In some embodiments,when the arc current is increased to a pulse value, the cathode chamberpotential drop U_(C-E1) may reach a peak 178. In some embodiments, arelatively higher value of voltage may increase the ion concentration tothe level corresponding to pulse arc current. In some embodiments, ifthe interval duration τ_(i) is shorter than the time of plasmarecombination, then a low voltage peak may be observed since the ionconcentration at the start of the pulse is higher. As shown in FIG. 67 ,for shorter interval duration the peak of the cathode chamber potentialdrop U_(C-E1) may be indeed lower.

With reference to FIG. 68 and the discussion above, base voltage U₁refers to the cathode chamber potential drop U_(C-E1) at point 176 whenthe interval duration τ_(i) may be substantially longer than plasmarecombination time. Residual voltage U_(res), calculated as a differencebetween base voltage U₁ and the voltage value at the point 176, may beused to estimate the plasma recombination time. Peak-to-base voltageU_(p-b), calculated as difference between peak voltage and base valueU₁, may characterize the difference between required ion concentrationfor the pulse arc current and ion concentration at the start of the arccurrent pulse.

FIGS. 69 and 70 demonstrate measured residual voltage U_(res) andpeak-to-base voltage U_(p-b) depending on interval duration τ_(i) forthe fixed pulse shape and amplitude and base arc current in range ofbetween about 3A to about 6 A. As shown in FIG. 69 , the residualvoltage U_(res) may decrease for longer interval duration τ_(i) andcharacteristic time of plasma recombination may be estimated as betweenabout 20 μs and about 40 μs in some embodiments. It may be noted thatplasma recombination time may be related to dissipation of excess ofplasma heat. Thus, it may depend on cathode chamber diameter and anefficiency of cooling. The fixed shape and amplitude of current pulsesmay result in the same ion concentration at the end of the currentpulse. For lower values of base arc current, the fixed ion concentrationat the end of current pulse may result in higher fraction of ion currentwhen arc current drops to base level. As consequence, the residualvoltage U_(res) may reach higher values for lower values of base arccurrent. Similarly, FIG. 70 demonstrates that for short intervalduration τ_(i), peak-to-base voltage U_(p-b) may be comparatively low,thus indicating that plasma did not recombine during this period. Theobserved high values of peak-to-base voltage U_(p-b) for lower base arccurrent may be a direct result of a greater difference between ionconcentration at the start of the arc current pulse and ionconcentration corresponding to pulse value of arc current.

In some embodiments, the minimum of the cathode chamber potential dropU_(C-E1) at point 174 may be due to a higher fraction of ion currentobserved and a comparatively slow current decrease rate of 6 A/ms. Thismay indicate that the detrimental process of “additional” cathodeheating due to shift of energy balance occurs when arc current isdecreased. The detrimental process may not be completely avoided sincethe surrounding plasma cannot be immediately removed or recombined atthe end of the current pulse. Therefore, for practical applications, theintensity of this detrimental effect may be decreased, and efficientcooling of the cathode may be realized. For example, the intensity ofthis detrimental effect may be reduced by decreasing ion concentrationor temperature in the vicinity of the cathode surface.

FIG. 71 illustrates a schematic of ion concentration distribution forstationary I₁ and I₂ currents. Due to recombination of ions at thecathode surface, the ion concentration may be lower in the thinnear-cathode layer or cathode sheath. In some embodiments, the ions maydiffuse to the cathode sheath from the adjacent layer. For simplicity ofexplanation, the surrounding concentration may be considered constant.In some embodiments, at near-cathode area thermodynamic characteristics,which includes ion concentration, may be different from plasma. Thenear-cathode area, also known as the non-equilibrium layer, is differentfrom plasma that may be in a local thermodynamic equilibrium. In someembodiments, the non-equilibrium layer may be divided into severalsublayers that includes: (1) a cathode sheath where emitted electronsmay be accelerated and ions recombine on a cathode surface; and, (2) anionization zone where emitted electrons ionize the plasma-generatinggas.

In some embodiments, as shown in FIG. 71 , the arc current may heat thesurrounding plasma and relatively higher current may correspond to arelatively higher degree of ionization of plasma, thus increasing theion concentration. When the current is rapidly changed from I₂ to I₁,the ion concentration may not drop immediately in contrast to current,and may contribute to a higher fraction of ion current to a cathodesurface. This may result in higher heat flux to the cathode. Increasingion current may provide redaction of emission electron from a cathodesurface and reduction of cooling. Over many cycles of currentoscillation, a small imbalance in heat flux may correspond tooverheating of the cathode and failure. In some embodiments, higher ionconcentration may bring higher ion current to the cathode and a highertemperature. Therefore, each ion may bring more thermal energy to thecathode.

In some embodiments, a cathode chamber may be configured to avoidcathode overheating when predominantly radially expanded andvolumetrically oscillating plasma is generated. This may require coolingof the cathode including efficient cooling of a cathode body andminimizing input heat flux to the cathode. Input heat flux may bereduced by decreasing an ion concentration in the proximity of cathodeactive area. In some embodiments, with reference to FIG. 56 , a diameterof cathode chamber 5560 and specifically its cylindrical portion 5562(e.g., d_(cc)) may be increased relative to a diameter of heatingchannel 5524 (e.g., d_(h)). Therefore, the plasma temperature and hencethe ion concentration in the proximity of a cathode active area may belower compared to the heating channel. FIG. 72 illustrates ionconcentration distribution depending on various ratios of d_(cc)/d_(h).Region I in FIG. 72 may refer to an ion concentration in a cathodechamber. Region II corresponds to ion concentration in the heatingchannel. This concentration may be defined by an average value of plasmatemperature in the heating channel and may correspond to about 16,000 Kin FIG. 72 . The displayed lines correspond to d_(cc)/d_(h) ratios of 1,2, 3 and 4. In some embodiments, the ion concentration drops about oneorder of magnitude when a d_(cc)/d_(h) ratio is increased from 1 to 4.

FIGS. 73 and 74 correspond to oscillograms for respective embodimentswith cathode chambers of different diameters (dcc/dh ratio may be 2 and4 for FIG. 73 and FIG. 74 , respectively). The oscillograms display avoltage A, current B, and power density C measured for relatively highfrequency current pulses. The voltage was measured between cathode 5506and first intermediate electrode 5510 to estimate the potential changein proximity of cathode active area. In some embodiments, theplasma-generating device with a d_(cc)/d_(h) ratio of about 2 fails togenerate plasma within first several minutes of operation while thegenerator with a d_(cc)/d_(h) ratio of about 4 may smoothly operate forhours. In both cases, the voltage behavior may be similar to voltageoscillation 162, as described with reference to FIG. 66B. However, thepower density for the exemplary embodiment of FIG. 74 ) may be one orderof magnitude lower than average. It should be noted that the displayedpower density may correspond to a total energy density that includesheating of a cathode, plasma in cathode chamber and a small portion of aheating channel. In some embodiments, significant electrode degradationmay correspond to oscillating current in contrast to constant currentoperation. At a constant current, relatively high heat energy deliveredto the cathode by ion bombardment may be proportionally balanced by ahigher number of emitted electrons. As mentioned above, in case ofoscillating current, the rapid decrease in current may correspond to ahigher fraction of ion current that brings more heat to the cathode fora duration of time corresponding to plasma recombination to a degree ofionization related to a lower arc current value.

FIG. 75 show a conductivity B oscillogram for relatively high frequencycurrent pulses. In some embodiments, the conductivity may be estimatedas an average value based on cathode chamber geometry. The graphdepicted in FIG. 75 is a qualitative estimation of conductivity. Thereal (e.g., actual or measured) conductivity may depend on arc shape andmay vary across the axis of a plasma-generating device (e.g., 100, 5500,5700). The observed peak in conductivity right after a current drop mayindicate an increased ion current fraction to the cathode surface.During this interval of time, the heat delivered to the cathode surfacemay be significantly larger for a d_(cc)/d_(h) ratio of about 2 incomparison to a d_(cc)/d_(h) ratio of about 4.

In some embodiments, the additional heating of cathode 5506 may occurwhen arc current demand is decreased. In some embodiments, an increasein cathode chamber diameter may reduce the ion concentration and iontemperature in a vicinity of a cathode surface, thus reducing thedetrimental effect of cathode overheating. In some embodiments, arelatively larger cathode chamber diameter may result in longer plasmarecombination time in the cathode chamber since excess plasma heat maydissipate mainly through the cathode chamber wall. In some embodiments,despite an increase of plasma recombination time, a larger diameter of acathode chamber may improve a lifespan of the plasma-generating devicesas shown in Table 2.

In some embodiments, an electric arc attachment may correspond to adegradation mechanism of a cathode. The arc attachment may be generallyrelatively narrower than the arc column 182, or more specificallytransverse geometrical dimensions of the arc. Current transfer fromthermionic cathodes to an arc plasma may occur in various ways. In someembodiments, there may be two distinguished modes: the spot attachmentwhere near cathode current may be localized in one of more relativelysmall areas as shown in FIGS. 76A and 76B, and a diffuse mode where nearcathode current is distributed over a larger area of cathode surface asshown in FIGS. 76C and 76D. For a spot attachment, the cathodetemperature on the spot surface may be considerably higher compared tothe cathode body. In the diffuse mode, an amount of the attachmentsurface increases relative to the spot attachment and plasma canpenetrate inside a ceramic insulator and increase a current density ofarc in a cathode region. In some embodiments, higher current density canincrease temperature and a plasma concentration around the cathodesurface during a pulse duration. Accordingly, in some embodiments, acathode may receive a more intensive ion current when the pulse currentdrops to a low base value and reduces electron emission current to coolthe cathode.

When the cathode is cold, the area of attachment may be relativelysmall. After several high frequency current pulses, the temperature ofthe cathode may increase so that during the period of a rapid currentincrease, the area of the attachment may expand over the entire surfacearea of the cathode and even to the cathode surface inside ceramicinsulator 154 as shown in FIG. 76E. Under these circumstances, the powerdensity and ion concentration in the vicinity of cathode surface that isinside the insulator sleeve 5554 (see FIGS. 55-56 ) may bring additionalheat by ion and returned electrons current from plasma. After apredetermined period of time, intensive cathode erosion may begin.Therefore, to maintain the proper functionality of the cathode, it maybe necessary to control the exact location and the size of the area ofthe electric arc attachment to the cathode surface during the periods ofrapid current increase and fall in each high frequency pulse of plasma.

In some embodiments, a plasma-generating device (e.g., 100, 5500, 5700)configured to operate with oscillating arc current may be characterizedbased on performance experiments and a discussion of possibledetrimental effect of cathode overheating due to shift of energybalance.

First, with reference to FIGS. 55 and 56 , the ratio of the diameter ofcathode chamber 5560 and specifically a cylindrical portion 5562 (e.g.,d_(cc)), and the diameter of heating channel 5524 (e.g., d_(h)) may beat least about 4.

$\frac{d_{cc}}{d_{h}} \geq 4$

This relationship may reduce plasma temperature and ion concentration inthe vicinity of a cathode surface, thus reducing (e.g., suppressing) thedetrimental effect of ion bombardment. Additionally, the cathode tip maybe at a sufficient distance from a heating channel to avoid influence ofthe heating channel on plasma temperature and ion concentration near acathode active area. This relationship may correspond to anotherrelationship.

Second, the ratio of the distance between cathode tip end point 5536 andthe heating channel inlet 5516 (e.g., I_(TH)) (tip to heat channeldistance), and the diameter of heating channel 5524 (e.g., d_(h)), maybe at least about 1.5.

$\frac{l_{TH}}{d_{h}} \geq 1.5$

In some embodiments, the insulator sleeve 5554 may be configured to coolthe cathode body by an inlet gas. The geometric relationships for theinsulator sleeve may be correspond to an arc attachment to the cathodesurface.

In some embodiments, the electric arc may have a spot attachment modeand the spot may be located at cathode tip end point 5536 on a surfaceof cathode 5506. In some embodiments, a diffuse mode attachment may benot desirable since arc attachment and plasma may enter inside insulatorsleeve 5554 and even deteriorate a cathode holder. In some embodiments,switching to a diffuse mode may occur when a large area of the cathodehas reached a predetermined high temperature to emit a considerablenumber of electrons from larger area. In some embodiments, to avoidswitching to a diffuse mode, the non-tip portion and some of the tipportion of cathode may be cooled.

In some embodiments, the efficiency of cathode cooling by an inlet gasmay depend on an inner diameter of insulator sleeve 5554. In someembodiments, a smaller diameter may be preferable in some applicationsbecause a gas speed inside the insulator sleeve may be higher, thusreducing the time of heat exchange between gas and cathode. As a result,a cooler gas may reach the end of cathode tip. Moreover, a relativelylarger diameter may result in a larger difference between gastemperature in a direction transverse to an axis of theplasma-generating device 5500. As a result, for a larger diameter, theheated gas may propagate along the cathode surface while a cooler gasmay propagate along the surface of insulator sleeve 5554. In someembodiments, the lowest limit of an insulator sleeve inner diameter maybe governed by a hydrodynamic drag of inlet gas that substantiallyincreases with a decreasing gap between cathode 5506 and insulatorsleeve 5554.

In some embodiments, a position of insulator sleeve 5554 may have rolein cathode cooling. If the end of insulator sleeve may be located closeto cathode tip end point 5536, it may be equivalent to reducing thecathode chamber diameter in proximity of arc attachment spot. Asdiscussed above, this undesirable situation may correspond to cathodeoverheating. In contrast, if the end of insulator sleeve may be locatedfar away from cathode tip end point 5536, the efficiency of cathodecooling may be decreased. The optimal conditions for the positioning ofinsulator sleeve was found experimentally based on performance tests asdiscussed above. Based on the described factors, efficient cooling ofcathode body may be accomplished by the following conditions.

First, the ratio of the length of the portion of cathode tip protrudingbeyond the distal edge 5556 of insulator sleeve 5554 l_(p) to thecathode 5506 diameter (cylindrical part of cathode) d_(c) may be in therange of between about 0.0 and about 1.6.

$1. \leq \frac{l_{p}}{d_{c}} \leq 1.6$

Second, the ratio of the cathode tip 5534 length (h) to cathode 5506diameter (cylindrical part of cathode) d_(c), may be in the range ofbetween about 1.5 and about 2.0.

$1.5 \leq \frac{l_{T}}{d_{c}} \leq 2.$

In some embodiments, for a predetermined range of plasma flowtemperature required for medical applications, the followingrequirements related to the heating portion of the plasma-generatingdevice may be met:

First, the diameter of the heating portion, dh may be in the range ofbetween about 0.4 mm and about 1.0 mm. Second, the ratio of the lengthof the anode portion of the plasma channel length, I_(anode) to thediameter of the anode portion of the plasma channel, d_(anode), may bein the range of between about 2 and about 4.

$2 \leq \frac{l_{anode}}{d_{anode}} \leq 4$

Third, for surgical applications, the diameter of the anode portion ofthe plasma channel may be the same as the diameter of the outlet in theabove discussion, d_(out), that is in the range of between about 0.3 mmand about 0.6 mm.

Turning back to the dimensions of the cathode chamber, it may bedesirable in some embodiments to maximize the diameter of cathodechamber 5560. If the plasma-generating device has an outer diameter ofabout 5 mm (a size suitable for laparoscopic surgery), the maximumdiameter of the cathode chamber may be about 1.8 mm. Larger diametersmay modify the structural integrity of other elements.

It is noted that the dimensions described herein merely constituteexemplary embodiments of the plasma-generating device and may be variedaccording to the field of application and the desired plasma properties.

Current Control Power Supply

According to the methods of generating predominantly radially expandedplasma flows described herein, the shape of resulting plasma flow may bemodified by varying the radial expansion degree along the axis of plasmajet. The conditions of radial expansion may be modified within shorttime intervals for dynamic control of a shape of a plasma jet. In someembodiments, thermal energy of individual plasma particles may beadjusted to a predetermined range of energies by regulating the baseplasma or target temperature of plasma.

In some embodiments, dynamic control of a plasma jet shape, temperature,and heat flux may improve thermal plasma-based technology. For example,dynamically controlled plasma flow may solve certain disadvantages ofplasma jets and enable complex material treatment procedures. Someplasma jets may have poor precision and non-uniform impact on treatedmaterial for turbulent flows and high radial temperature gradient forlaminar plasma jets. Dynamic control of a plasma jet shape, temperature,and heat flux may independently and simultaneously solve certainproblems related to material treatment or processing such aswell-controlled heat transfer to the surface, vaporization, pyrolysis,cleaning, modification, etc.

Some embodiments of plasma-generating device may operate on a wide rangeand various conditions of oscillating current to generate plasma jetwith controlled shape and energy range of individual particles. In someembodiments, a current control signal having a high time resolution of acurrent change rate may be configured to control plasma shapegeneration. Some embodiments of a current control generator for aplasma-generating device may use one or more current patterns configuredto provide efficient and dynamic control of a plasma jet shape andenergy level. As discussed herein, applied current to theplasma-generating device may depend on geometric factors of aplasma-generating device and more specifically the diameter of a heatingchannel. In some embodiments, instead of using absolute value ofcurrent, the relationships for the current control generator may bebased on a ratio of current to diameter of a heating channel dm

With reference to FIG. 77 , relatively high frequency oscillation f_(HF)184 may refer to the frequency of current pulses that regulate plasmaflow expansion or plasma jet shape. As described herein, radialexpansion may be controlled based at least in part on the shape andamplitude of high frequency oscillation. In some embodiments, a basecurrent level 186 of relatively high frequency oscillations may definethe energy range of individual plasma particles. The energy range ofindividual particles is not the same as an energy range of heat fluxtransferred to the treated surface. In some embodiments, the energy ofindividual particles may be defined by the plasma temperature, while thetotal energy that may be applied to treated object may be defined byboth plasma temperature and plasma mass flux, i.e. the total energy mayinclude the sum of energies transferred by all the plasma particles. Insome embodiments, relatively low frequency oscillation fLF may refer tothe frequency of repetition of the complete pattern of the base currentlevel. The corresponding period of relatively low and high frequencyoscillation may be defined as 1/f_(LF) and 1/f_(HF), respectively. Asshown in FIG. 77 , the frequency, shape, and amplitude of high frequencyoscillation may vary for different parts of low frequency oscillation.

4. Medical Applications

In some embodiments, a plasma-generating device such that thosedescribed herein (e.g. plasma generating device 100, 5500, etc.) may beused in medical or surgical applications. In some embodiments, aplasma-generating device may be configured to apply predeterminedcurrent patterns suitable for different medical applications. In someembodiments directed to medical applications, a predominantly radiallyexpanded plasma flow may be used in combination with: (1) otherpredominantly radially expanded plasma flows; (2) radially expandedplasma flows having axial expansion; or (3) substantially continuousplasma flows.

In the following sections, several examples of medical applications aredescribed, with respective illustrations of plasma flow and/or currentpatterns suitable for generating such plasma flow. Many of theseprocedures and treated tissue applications can require individualinstruments, and some treatment may require synchronized and precisecontrol of vaporization and heat diffusion processes.

Table 3 includes a list of different types of procedures and treatedtissue, along with associated tissue properties and suitable powerranges for each. In some embodiments, the power range for a procedure,measured in W, may correspond to a predetermined plasma jet power leveland temperature profile to achieve a particular type of action for arespective procedure.

TABLE 3 Tissue properties and suitable power range for certain surgicalprocedures. Procedure description/ Tissue properties Suggested powertreated Intensity of blood Tissue Tissue range for a tissue flow onsurface density perfusion procedure, W Spot Coagulation low all typesmed 50-60 Lympho-sealing no all types all types 30-50 lung med very lowmed 50-65 spleen high low high 50-65 pancreas med low med 40-55 musclehigh med med 60-75 liver high med high  80-100 kidney high high high 80-100 Dissection pure high low high 25-65 Dissection blend high lowhigh 40-75 Vaporization pure med low med 40-65 Vaporization blend medlow med 45-75 Cut pure high med med 45-85 Cut blend high med med 50-90

Tables 4 and 5 summarize a set of suitable protocols (e.g., parametersettings or ranges) of a plasma-generating device for variousapplications. In each example, two types of plasma flows may begenerated: the relatively low intensity plasma flow with relatively lowtemperature TL base of the temperature-time profile, and the relativelyhigh intensity plasma flow with the relatively high temperature TH base.In some embodiments, the low intensity plasma flow may be apredominantly radially expanded plasma flow that may not destructtissue. In some embodiments, the high intensity plasma flow may be apredominantly radially expanded plasma flow, a radially and axiallyexpanded plasma flow, as well as a continuous plasma flow.

For Table 4, where current includes two base levels (e.g., low baselevel BL, high base level BH), a set of parameters may be understood asdescribed below. I_(BL)/d, A/mm may correspond to a ratio of low basecurrent level A to heating channel diameter mm. I_(BH)/I_(BL) maycorrespond to a ratio of a high level of base current to a low level ofbase current. I_(PL)/I_(BL) may correspond to a ratio LF pulse currentto a low level base current. I_(PL) may be associated with a LF pulselevel for low level base current. T_(LF), ms may correspond with aperiod of a low frequency current. D_(LF) may correspond to duty of lowfrequency current oscillation. T_(HFL), μs may correspond to a period ofa high frequency pulse current for a low level of base current. D_(HFL)may correspond to a duty of high frequency current pulses for a lowlevel of base current. T_(HFH), μs may correspond to a period of a highfrequency pulse current for a high level of base current. D_(HFH) maycorrespond to a duty of high frequency current pulses for a high levelof base current. T_(HFH), μs may correspond to a period of a highfrequency pulse current for a high level of base current. D_(HFH) maycorrespond to a duty of high frequency current pulses for a high levelof base current.

For Table 5, where current has a single base level, a set of parametersmay be understood as described below. I_(B)/d, A/mm may correspond to aratio of base current level A to heating channel diameter mm.I_(LF)/I_(B) may correspond to a ratio of LF pulse current to basecurrent. I_(HF)/I_(B) may correspond to a ratio of HF pulse current to abase current. T_(LF), ms may correspond to a period of low frequencycurrent. T_(HF), μs may correspond to a period of high frequency pulsecurrent. D_(LF) may correspond to a duty of low frequency currentoscillation. D_(HF) may correspond to a duty of high frequency currentpulses.

TABLE 4 Parameters for certain surgical procedures using current havingtwo base levels, i.e., low base level (BL) and high base level (BH)Procedure Gas description/ Flow, I_(BL)/d, I_(BH)/ I_(PL)/ T_(LF),T_(HFL), T_(HFH), tissue L/min A/mm I_(BL) I_(BL) ms D_(LF) μs D_(HFL)μs D_(HFH) Spot  0.4-0.55  7.5-10 0.1-0.7 2.5-5  5-20  0.4-0.6 20-500.3-0.6 20-50 0.3-0.6 Coagulation Lympho-  0.3-0.5  7.5-10 1.5-4 2.5-530-40  0.1-0.2 20-50 0.3-0.6 20-50 0.3-0.6 sealing lung  0.2-0.3  7.5-102.5-5 2.5-5 30-40  0.1-0.2 20-50 0.3-0.6 20-50 0.3-0.6 spleen  0.2-0.3 7.5-10 1.7-3 2.5-5 25-35  0.1-0.15 20-50 0.3-0.6 20-50 0.3-0.6 pancreas 0.2-0.3  7.5-10   1-2 2.5-5 25-35  0.1-0.15 20-50 0.3-0.6 20-50 0.3-0.6muscle 0.35-0.45  7.5-10 1.2-2.3 2.5-5 30-35 0.05-0.1 20-40 0.3-0.620-40 0.3-0.6 liver  0.4-0.5  7.5-10 2.5-4 2.5-5 30-40  0.1-0.15 20-500.3-0.6 20-50 0.3-0.6 kidney 0.45-0.55  7.5-10 2.5-5.3 2.5-5 20-250.05-0.1 20-50 0.3-0.6 20-50 0.3-0.6 Dissection 0.15-0.3   10-12.5 1.2-3  1-2  5-10  0.1-0.2 20-50 0.3-0.6 20-50 0.3-0.6 pure Dissection0.15-0.3   10-12.5 1.4-3.2 1.4-2.5  5-10  0.1-0.2 20-45 0.4-0.6 20-450.4-0.6 blend Vaporization  0.2-0.3 12.5-15 1.7-3 1.0-1.4  5-15 0.1-0.15 30-50 0.3-0.6 30-50 0.3-0.6 pure Vaporization  0.2-0.3 12.5-151.7-3   1-1.6  5-15  0.1-0.15 20-40 0.4-0.6 20-40 0.4-0.6 blend Cut pure 0.2-0.35 12.5-16.2 0.7-1.4 1.0-1.6  5-10 0.15-0.25 30-45 0.3-0.6 30-450.3-0.6 Cut blend  0.2-0.35 12.5-16.2 0.7-1.4 1.2-2  5-10 0.15-0.2520-40 0.4-0.6 20-40 0.4-0.6

TABLE 5 Parameters for certain surgical procedures using current withsingle base level Procedure Gas description/ Flow, I_(B)/d, T_(LF),T_(HF), tissue L/min A/mm I_(LF)/I_(B) I_(HF)/I_(B) ms μs D_(LF) D_(HF)Spot  0.4-0.55  7.5-10 0.13-0.67 2.5-5  5-20 20-50  0.4-0.6 0.3-0.6Coagulation Lympho-  0.3-0.5  7.5-10  1.5-4 2.5-5 30-40 20-50  0.1-0.20.3-0.6 sealing lung  0.2-0.3  7.5-10  2.5-5 2.5-5 30-40 20-50  0.1-0.20.3-0.6 spleen  0.2-0.3  7.5-10 1.75-3 2.5-5 25-35 20-50  0.1-0.150.3-0.6 pancreas  0.2-0.3  7.5-10   1-2 2.5-5 25-35 20-50  0.1-0.150.3-0.6 muscle 0.35-0.45  7.5-10 1.25-2.33 2.5-5 30-35 20-40 0.05-0.10.3-0.6 liver  0.4-0.5  7.5-10  2.5-4 2.5-5 30-40 20-50  0.1-0.150.3-0.6 kidney 0.45-0.55  7.5-10  2.5-5.33 2.5-5 20-25 20-50 0.05-0.10.3-0.6 Dissection 0.15-0.3   10-12.5  1.2-3   1-2  5-10 20-50  0.1-0.20.3-0.6 pure Dissection 0.15-0.3   10-12.5  1.4-3.25 1.4-2.5  5-10 20-45 0.1-0.2 0.4-0.6 blend Vaporization  0.2-0.3 12.5-15 1.67-3 1.0-1.4 5-15 30-50  0.1-0.15 0.3-0.6 pure Vaporization  0.2-0.3 12.5-15 1.67-3  1-1.6  5-15 20-40  0.1-0.15 0.4-0.6 blend Cut pure  0.2-0.35 12.5-16.20.77-1.4 1.0-1.6  5-10 30-45 0.15-0.25 0.3-0.6 Cut blend  0.2-0.3512.5-16.2 0.77-1.4 1.2-2  5-10 20-40 0.15-0.25 0.4-0.6

FIG. 88 shows a generalized temperature-time profile that may be usedfor a variety of medical applications. The temperature-time profileshown in FIG. 88 largely tracks the diameter current-time profile shownin FIG. 87 . Referring to the discussion above, this temperature-timeprofile shows various base plasma flow temperatures at the outlet. Itmay be understood that each of the base temperatures may havecorresponding high-frequency high-temperature pulses “on top” of basetemperature plasma flows.

Experiments show that the delay between changing the current in thepower supply and changes in temperature may be in the order ofnanoseconds, and for the purposes of this discussion the changes in thetemperature of the plasma at the generator outlet may be consideredinstantaneous. Generally, tracking the current pattern, the basetemperature oscillates between low temperature TL and high temperatureTH. Low temperature TL may be in the range of between about 2,000 K andabout 15,000 K and high temperature TH may be in the range of betweenabout 4,000 K and about 30,000 K, but the low temperature TL may bealways lower than the corresponding high temperature TH. In other words,if the low temperature may be set to, for example, about 7,000 K, thenthe high temperature TH may be set to a temperature higher than about7,000 K, or for example, about 20,000 K.

In some embodiments, as shown in FIG. 88 , the low and high temperaturesmay not be uniform and may exhibit predetermined variations. For lowtemperatures, these variations may occur at about 5 ms intervals,although different intervals in the range of between about 1 ms andabout 10 ms may be contemplated. In some embodiments, the lowtemperature may correspond to up to about 10 variations, but in someembodiments, such as the one tracking the current pattern shown in FIG.79C, no low temperature variations occur. In some embodiments, themagnitude of low temperature variations may be in the range of betweenabout 500 K and about 1,000 K, but may depart from this range. For hightemperatures, these variations may occur at about 1 ms intervals, or inthe range of between about 0.2 ms and about 2 ms. In some embodiments,the high temperature may correspond to up to about 5 variations. In someembodiments, such as the one tracking the current pattern shown in FIG.83A, no high temperature variations occur. In some embodiments, themagnitude of high temperature variations may be in the range of betweenabout 1,000 K and about 2,000 K.

In some embodiments, and as shown in FIG. 88 , the time-temperatureprofile may be periodic with the period, for example, in the range ofbetween about 6 ms and about 65 ms. To distinguish the terminologyassociated with changes and oscillations of the base plasma flowtemperature among different values with temperature oscillations betweenthe base temperature and the pulse temperature, the followingterminology may be used. From the viewpoint of the plasma medicine, amedical procedure may be considered as causing a predetermined effect onthe tissue by the plasma flow. Continuous plasma flows may accomplish aprimary effect on the tissue, with other desirable outcomes being merelyside effects of the primary purpose for which the plasma flowcharacteristics have been chosen. For example, if a continuous plasmaflow has been chosen for cutting tissue, any coagulation or bloodvaporization effects that this continuous plasma flow may produce may becoincidental side effects.

In some embodiments, the use of temperature profiles such as in FIG. 88allows for the development of two or more plasma flows that may havedifferent intended effects on the tissue. Additionally or alternatively,in situations where the periodic effect of one type of plasma may bedesired, the second plasma flow may be generated for maintaining aplasma flow in in the handpiece while minimizing its effect on thetissue surface being treated by minimizing the plasma flow length byincreasing the frequency of high-frequency oscillations.

In some embodiments, a method may include discharging, from an outlet ofa plasma-generating device, a plasma flow having a directional axis, theplasma flow alternating between a first configuration including plasmahaving a first temperature higher than about 1,000 K between first andsecond points along the directional axis, the first point being closerto the outlet than the second point, and a second configurationincluding plasma having a second temperature higher than about 1,000 Kbetween third and fourth points along the directional axis, the thirdpoint being closer to the outlet than the fourth point and the fourthpoint being closer to the outlet than the second point. The plasma flowmay be directed at a treatment surface disposed between the second pointand the fourth point.

In some embodiments, discharging the plasma flow alternating between thefirst and second configurations includes discharging the plasma flow inthe first configuration for a first duration and discharging the plasmaflow in the second configuration for a second duration. In someembodiments, the first duration can be greater than the second duration,while in other embodiments, the second duration can be greater than thefirst duration.

In some embodiments, discharging the plasma flow in the firstconfiguration for the first duration may cause evaporation of liquidfrom the treatment surface and may not cause substantial damage to thetreatment surface. In some embodiments, the first duration may be aboutfive times the second duration. In some embodiments, the firsttemperature may alternate between first and second values, the firstvalue being lower than the second value, and the second temperature mayalternate between third and fourth values, the third value being lowerthan the fourth value and higher than the second value.

Vaporization, Sublimation, and Controlled Heating

The plasma-generating device described herein can be configured forthermal processing of the materials including, but not limited to,vaporization/sublimation of the object surface without heat transferinside the object (V/S), controlled heating of the material avoidingpotential damage of the object due to local overheating (CH), andcombined simultaneous V/S and CH treatment with precise control of bothprocedure (combined V/S & CH).

Generally, vaporization is a conversion of an object layer to gaseousform via evaporation, sublimation and pyrolysis. Vaporization of theobject surface without heat transfer inside the object may be useful forapplications such as cleaning, drying, and etching, since it allowsremoval of the layer of the treated object without damaging the rest ofthe material. Moreover, if the rest of the object is not heated duringthe procedure, it may not undergo thermal expansion such that noadditional mechanical tension is formed, thereby preserving the initialstructure of the object except for the vaporized layer.

In some embodiments, analysis of heat transfer of a treated surface mayhelp understand the parameters of the three procedures (V/S, CH andcombined V/S and CH). In some embodiments, the heat flow transferred tothe object surface may depend on plasma jet temperature and mass flux atthe surface. In some embodiments, the heat flux may be calculated basedon the formula:

q=h(g_(js))(T_(j)-T_(o))   (46)

where h(g_(js)) is a heat transfer coefficient that may be directlyrelated with plasma mass flux g_(js) at the object surface. T_(j) may bea plasma jet temperature at the surface.

In some embodiments, plasma mass flux g_(js) at the object surface maybe estimated based on an outlet mass flux and ratio of plasma jetcross-sectional area at the nozzle outlet and object surface.

$g_{js} \approx {\frac{A_{o}}{A_{s}}g_{jo}}$

where A_(o), A_(s) is a cross section area transverse to the plasma jetaxis at the nozzle outlet and at the object surface, respectively.g_(jo) is a mass flux at the nozzle outlet.

In some embodiments, the heat transfer coefficient h(g_(js)) may be acomplex function of mass flux. For the sake of simplicity, the heattransfer coefficient may be considered to be proportional to mass flux.In this case, the heat flux may be estimated based on the followingexpression:

$\begin{matrix}{q = {H^{*}\frac{g_{jo}}{A_{s}}\left( {T_{j} - T_{o}} \right)}} & (47)\end{matrix}$

In some embodiments, the heat flux to the object surface may bothvaporize the surface layer and diffuse inside the object. In someembodiments, the heat equation may be given by:

$\begin{matrix}{q = {{H^{*}\frac{g_{jo}}{A_{s}}\left( {T_{j} - T_{o}} \right)} = {{\rho E_{v}U_{v}} - {\lambda\frac{\partial T}{\partial z}\left( {z = 0} \right)}}}} & (48)\end{matrix}$

where ρ, λ is density and thermal conductivity of the object, E_(v) isspecific energy of vaporization and U_(v) is a vaporization rate thatmay defines how fast the object surface location moves due tovaporization of the material.

$\frac{\partial T}{\partial x}\left( {z = 0} \right)$

is a temperature gradient at the surface.

In some embodiments, since the diffusion rate may be defined bytemperature distribution in the vicinity of the surface, vaporizationmay be dominant. In some embodiments, if a vaporization rate iscomparable with diffusion heat transfer, then vaporization of thetreated object without heating the rest of the object may be achieved.In some embodiments, the thickness of the removed layer during timeinterval Ar may be calculated as L_(v)=U_(v)·Δτ. For the same timeinterval, a penetration length of heat into the treated object may beestimated as L_(d)=√{square root over (4·k·Δτ)}, where k is thermaldiffusivity of the treated object. Based on these estimations, FIG. 78depicts that a ratio of vaporized layer thickness to heat penetrationlength may substantially decrease with higher values of vaporizationrate. As a result, vaporization of an object surface without heattransfer inside the object may require a high vaporization rate (e.g.,about 100 mm/s) that may be achieved by a high heat flux to the surface.A plasma jet generated at a constant current having a vaporization rateof about 100 mm/s may not be practical for many applications. Forexample, some surgical applications may require an average vaporizationrate in range of between about 0.01 mm/s and about 2 mm/s.

In some embodiments, an average vaporization rate may be reduced byapplying short pulses of high temperature plasma as shown in FIG. 79A.In some embodiments, the average vaporization rate may be adjusted bythe duty of the pulses, which may be a ratio of pulse duration to periodof pulse repetition. In some embodiments, the vaporization depthresolution may be defined by the minimum possible duration of thepulses. However, such an approach may have drawbacks. First, forrelatively low vaporization rates, the pulse duration may beconsiderably shorter. For a vaporization depth of about 0.5 mm, thepulse duration may be no more than about 5 ms, and may be shorter ifbetter vaporization depth resolution is desired. In some embodiments,ignition of plasma with subsequent heating to high temperature and pulseduration less than about 5 ms may have technical difficulties. Second, apredetermined mass flow for pulses may be generated to achieve high heatflux to the surface. According to Eq. 5 and Eq. 10, the inlet gas flowmay be considerably higher to provide the required gas flow for thepulses with low duty to correspond to substantial consumption of gasbetween pulses that might be not desirable. For example, high mass fluxmay build excessive pressure for a small nozzle diameter. Alternatively,the working pressure may be pumped up during a pulse duration, but itmay significantly complicate the system. Third, this approach targets avaporization procedure of the material treatment. However, implementingadditional procedures of treatment that involve controlled heatdiffusion may require additional modifications.

FIG. 79B depicts a base current level between pulses configured tomaintain the electric arc in the plasma-generating device and whichaddresses issues related to plasma ignition. In some embodiments, if theelectric arc is maintained, the pulse duration may be substantiallylower, thus improving vaporization depth resolution. In someembodiments, the base current level between pulses may also help buildup working pressure. FIG. 80 shows that when the current pattern ischanged from A to B (FIG. 79 ), the working pressure may increase fromP_(W) ^(A) to P_(W) ^(B) and the pulse outlet mass flux may increasefrom g_(jo) ^(Pulse(A)) to g_(jo) ^(Pulse(B)). In some embodiments, theincrease of pulse outlet mass flux may also be beneficial since a highervaporization rate and hence better conditions for a vaporizationprocedure (V/S) may be achieved, as may be seen from Eq. 48. However,the relatively low current level between pulses may also generate aplasma jet of relatively lower temperature that may generate undesirableheat diffusion inside the treated object.

With reference to FIG. 81A, the term “high intensive plasma jet” refersto a plasma jet, that may be formed during current pulses and depictedby curve 188. The term “low intensive plasma jet” may refer to plasmajet, that may be formed between current pulses and depicted by curve190. Because of high temperature of plasma particles, the high intensiveplasma jet may have a longer longitudinal size and may be used forvaporization procedure without heat transfer inside the object. At thesame time, low intensive plasma may have a shorter longitudinal size,thereby bringing undesirable heat transfer inside the object. In someembodiments, the zone II depicted in FIG. 81A may be used for avaporization procedure. It should be noted that since the plasma jetshape may be defined by a temperature threshold, there may be heat fluxoutside of the depicted plasma jet. As a result, low intensive plasmamay bring undesirable vaporization heat flux in zone II. Moreover, theimpact of low intensive plasma on zone II may worsen based on a highmass flux g_(jo) ^(Base(B)) between the pulses (see FIG. 80 ).

In some embodiments, vaporization of the object surface without heattransfer inside the object may include avoiding the impact of lowintensive plasma 190. In some embodiments, this may be achieved byreducing heat flux to the surface by low intensive plasma. According toEq. 47, the heat flux may depend on one or more of jet temperatureoutlet heat flux g_(jo), and a plasma jet shape, or more specificallythe cross-sectional area transverse to the plasma jet axis at the objectsurface A_(s). In some embodiments, outlet heat flux and jet temperatureof low intensive plasma may have a complex relationship with highintensive plasma where optimization may correspond to lower values ofbase current limited by minimal arc current and degradation processes ofa plasma-generating device. In some embodiments, an increase in atransverse cross-sectional area of a low intensive plasma jet maysubstantially reduce the undesirable heat transfer inside the object.However, the plasma jet shape may not be independently changed for highand low intensive plasma in case of laminar or turbulent flow.

In some embodiments, plasma jet shape control may reduce the negativeeffect of low intensive plasma for vaporization procedures. Apredetermined plasma jet shape may be obtained by adding the highfrequency oscillation of current on top of the current pattern as shownin FIG. 79C. The radial expansion of the low intensive plasma may besufficiently high to suppress the heat flux of low intensive plasmatowards zone II. As shown in FIG. 82A, the resulting low intensiveplasma jet 192 has a high degree of radial expansion. Thus, vaporizationprocedure without heat transfer inside the object requires considerablylower radial expansion of low intensive plasma and treated object may belocated in the zone II as shown in FIG. 82A.

The jet shape of high intensive plasma may be also controlled by addingsmaller degree of radial expansion. As previously mentioned, the radialdegree may be adjusted by the shape of high frequency oscillation ofcurrent. For example, jet shapes 194 and 196 demonstrate two possibleplasma jet shapes of high intensive plasma based on corresponding highfrequency current oscillation.

In case of additional high frequency oscillation, the terms high and lowintensive plasma may be clarified. The term “low intensive plasma jet”may refer to shapes of plasma jet formed with relatively low basecurrent 192. The term “high intensive plasma jet” may refer t all shapesof plasma jet that may be formed with relatively high base current 194,196.

In some embodiments, a system may include a current generator configuredto generate a current having a controlled pattern. The controlledpattern may include a first set of oscillations between a first baselevel and a first pulse level, the first pulse level being higher thanthe first base level, and a second set of oscillations between a secondbase level and a second pulse level, the second pulse level being higherthan the second base level. A plasma-generating device may be configuredto heat, in response to the current being applied to a heating portionof the plasma-generating device, a plasma-generating gas to generate aplasma flow within the plasma-generating device. The plasma flowalternating between a first configuration having a first degree ofradial expansion and a second configuration having a second degree ofradial expansion may be discharged from an outlet of theplasma-generating device, according to the controlled pattern of thecurrent.

In some embodiments, the second base level may be greater than the firstbase level, and the second pulse level may be greater than the firstpulse level. In some embodiments, the heating portion may include aheating channel, and a diameter of the heating channel may be no morethan about 0.4 mm. In some embodiments, a diameter of the outlet may begreater than a diameter of the heating channel. In some embodiments, thefirst degree of radial expansion may be greater than the second degreeof radial expansion. In some embodiments, the plasma flow may include anactive zone defined by plasma having a temperature above about 1,000 K,the active zone having a diameter that may be at least ten times greaterthan a diameter of the outlet.

In some embodiments, a current pattern may be improved for vaporizationprocedure by adding light oscillation of base current level for lowintensive plasma as demonstrated in FIG. 83A. With reference to themethods, this additional oscillation of base current level may haveseveral beneficial functions. First, working pressure may increase whichmay in turn increase heat flux for high intensive plasma to therebyenhance the evaporation rate. Second, radial expansion conditions of lowintensive plasma may be improved. Third, the detrimental effect ofcathode overheating may be lowered due to efficient increase of basecurrent level.

In some embodiments, a procedure may include treating a sample with heatresulting in minimal or no damage to the treated sample due to localoverheating. In some embodiments, a current pattern may include lowintensive plasma jet with considerably high radial expansion is shown inFIG. 83B. Such a current pattern may be necessary to shift balance inthe Eq. 48 towards predominant diffusion of heat flux inside a treatedobject. In some embodiments, a low level of base current may be used toreduce total heat flux and suppress vaporization process. In someembodiments, a diffusion rate may be adjusted by the inlet gas flow. Asdescribed herein, low frequency oscillation of base current level mayplay a positive role by improving conditions for radial expansion anddecreasing negative effect of cathode overheating.

In some embodiments, vaporization and controlled heating treatment maybe applied in procedures for homogenous objects. In some embodiments, atreated object may be heterogenous and controlled vaporization andheating may be used to achieve a desired effect. In some embodiments, asequence of vaporization and controlled heating may be performed withvarious degrees for each treatment step. For surgical applications, aprocedure might include simultaneous controlled vaporization and heatingthat targets one or more of drying of incoming flows of physiologicalliquids such as blood and lymph, tissue coagulation, vascular occlusionand coagulation (that might require penetration of plasma flow insidethe open blood vessel), and tissue cutting.

In some embodiments, a predetermined current pattern may be applied to aplasma-generating device. The current pattern structure may include alow frequency oscillation of base current level and high frequencyoscillation on top of base current level configured to adjust radialexpansion of a plasma jet. In some embodiments, a base current level maybe schematically divided into low and high base current levels forcorresponding low and high intensive plasma jets. High intensive plasmajets may be responsible for moderate and predominant vaporization whilelow intensive plasma jets may be applied for moderate or predominantheat diffusion inside a treated object. As shown in FIG. 84 , both highand low base current levels may include one or more parts with differentbase current and high frequency shape. In FIG. 84 , HI-1 and HI-2 referto parts of a current pattern that may result in corresponding highintensive plasma jets. Similarly, LI-1 and LI-2 refer to currentpatterns and corresponding low intensive plasma jets.

In some embodiments, the number of various parts of a current pattern,the duration of each of these parts and corresponding plasma jets may beadjusted to target specific application or procedure. For example, thedepicted current pattern structure in FIG. 84 may be useful for somesurgical procedures having tissue coagulation with various sizes of openblood vessels. High intensive plasma jet HI-2 with moderate radialexpansion may result in blood drying, low intensive jets LI-1 and LI-2may need to coagulate the dried tissue, and high intensive jet HI-1 withlow radial expansion may penetrate deeper in the open blood vessel andresult in occlusion and coagulation.

In some embodiments, one or more parts of a current pattern may beresponsible for generating a plasma jet shape that may target a specificaspect of object treatment. In some embodiments, a current pattern mayinclude two beneficial features. First, as previously discussed, lightoscillation of low base current level may build up working pressure anddecrease the detrimental effects of cathode overheating. This type ofoscillation of base current level may be shown as LI-1 and LI-2 in FIG.84 . Second, for high and low frequency oscillation, a current drop ratemay slow down towards the end of the current pulse as schematicallydemonstrated in FIG. 85 . This shape of current may reduce a negativeeffect of cathode overheating due to slower rate of current decrease.Slowing down the drop rate at the end of current pulse may also resultin a gradual reduction of plasma temperature and flow velocity. Asdiscussed with respect to predominantly radially expanded plasma flows,the initiator plasma flow may slowly reduce its flow velocity, thusleading to efficient increase of pulse duty and better condition foroptimal radial expansion.

In some embodiments, control of a current pattern structure may cover aset of object treatment procedures including controlled vaporization andcontrolled heat diffusion based on combinations of various plasma jetshapes with tunable radial expansion. In some embodiments, a currentcontrol generator for a plasma-generating device may have one or moreprocessors that may meet the current output relationships including, butnot limited to, providing low frequency current oscillation with currentpulse resolution in a range of between about 0.1 ms and about 0.2 ms,providing high frequency current oscillation with current pulseresolution in a range of between about 0.1 μs and about 1 μs, andproviding synchronization of the high and low frequency currentoscillation.

In some embodiments, dynamic control of plasma jet shape and temperaturemay cover many types of complex procedures. Table 6 lists severalexamples with a variety of low and high intensive plasma jet shapes(FIG. 86 ) and typical vaporization and control heating procedures, thatmay be used with these shape combinations. In Table 6, “V/S” stands forvaporization procedure, “precision V/S” may refer to a smaller area ofvaporization comparable with a nozzle diameter, while a spot correspondsto a larger area of the treated object. Base characteristics describebase current level of current pattern structure such as low base currentlevel I_(BL); high base current level I_(BH); duty D_(LF) and periodT_(LF) of low frequency pulses. Low and high intensive jetcharacteristics may describe parameters of high frequency oscillationfor low and high intensive plasma jets, namely for low and highintensive jets, respectively, the pulse currents of high frequencyoscillation may be designated as I_(PL) and I_(PH), duty is D_(HFL) andD_(HFH), period of oscillation T_(HFL) and T_(HFH).

In FIG. 86 , the high intensive plasma jet may be depicted by blacklines and low intensive plasma jet may be depicted by gray lines. Asshown in FIG. 86 , for vaporization procedures (“V-1”-“V-4”) the highintensive jet (black lines) may be longer and may be with differentdegrees of radial expansion, that may be as low as for laminar flow. Atthe same time, low intensive plasma jets (gray lines) may beconsiderably shorter to reduce or avoid the heat diffusion inside thetreated object. In some embodiments, vaporization procedures may havesubstantially higher radial expansion and shorter distances for lowintensive plasma jet compared to a high intensive jet. As previouslydiscussed, the higher frequency may result in a shorter jet length.Therefore, for vaporization procedures, it may be desirable to have ahigher frequency of oscillation for high intensive jet, i.e.f_(HFL)>f_(HFH) (T_(HFL)<T_(HFH)). Also, for a higher radial expansiondegree, the high frequency oscillation amplitude may be higher for lowintensive plasma (I_(PL)<I_(PH)). In some embodiments, the low frequencypulse amplitude I_(BH) may be considerably higher than low frequencybase amplitude I_(BL).

As for controlled heating procedures (“CH-3”-“CH-6”), the high intensiveplasma jet may be considered as a low intensive plasma jet with aslightly higher value of base current or more specifically, basecurrents IBH and IBL may be both low intensive plasma jets with aslightly different base current level that help boost up workingpressure. In some embodiments, for controlled heating, it may bebeneficial to not have high temperature plasma jet that would result inpartial vaporization. In this case, the term “high intensive plasma jet”may be used for consistency of comparison to vaporization procedure, andalso may be useful in terms of generalized current pattern structure forany type of procedures. To avoid local overheating, the radial expansionmay be comparatively high for both low and high intensive plasma jet.

In some embodiments, more complex procedures may be achieved by tuningthe shapes, temperature range, and duration for both high and lowintensive plasma jets. The plasma jet shape adjustment may involve theradial expansion degree along the jet axis. For example, the radialexpansion may be high in the middle and low at the distal end of plasmajet.

TABLE 6 Set of example plasma jet shapes, corresponding procedures andpredetermined current pattern parameter range. Vaporization proceduresControlled heating Precision V/S Precision V/S Large spot V/S Large spotSpot heating Spot heating Spot heating Spot heating w/o heat with lowheat w/o heat V/S with w/o V/S soft w/o V/S dense with V/S soft with V/Sdense diffusion impact diffusion low heat material material materialmaterial Base I_(BL)/d,  5-10 10-15  5-10 10-15 10-20 10-20 10-20 10-20A/mm I_(BH)/I_(BL)  5-20  5-20  5-10  5-10 1-2 1.5-3   2-5  3-10 D_(LF)0.05-0.15 0.05-0.15 0.05-0.15 0.05-0.15 0.02-0.1  0.02-0.2  0.02-0.1 0.05-0.2  T_(LF), 0.5-10  0.5-10  0.5-10  0.5-10  10-35 10-35 10-3510-35 μs Low T_(HFL), 25-50 35-50 25-50 35-50 35-50 35-50 35-50 35-50intensive μs jet D_(HFL) 0.1-0.3 0.1-0.3 0.1-0.3 0.1-0.3 0.1-0.3 0.1-0.30.1-0.3 0.1-0.3 I_(PL)/I_(BL)  5-20  3-10  5-20  3-10  3-10  3-10  3-10 3-10 High T_(HFH), not required not required 40-50 40-50 35-50 35-5035-50 35-50 intensive μs jet D_(HFH) not required not required 0.1-0.30.1-0.3 0.1-0.3 0.1-0.3 0.1-0.3 0.1-0.3 I_(PH)/ not require not require2-5 2-5  3-10  3-10 2-5 2-5 I_(BH) Plasma jet shape V-1 V-2 V-3 V-4 CH-3CH-4 CH-5 CH-6 (FIG. 86)

Lympho-Sealing

Systems, devices, and methods described herein can be used in alympho-sealing procedure. In some embodiments, a lympho-sealingprocedure may allow lymphatic drainage to be avoided during operation.In particular, lympho-sealing is a procedure in which the discharge oflymph may be stopped from a particular spot with minimal or no damage tothe surrounding anatomic structures. Image CH-1 and CH-2 of FIG. 86illustrate the resulting low and high intensive plasma jet shape forprecision or spot lympho-sealing procedure. The high intensive plasma(black lines) jet may generate the evaporation of lymph from the surfacebeing treated. Exposing tissue to high intensive plasma jet for a longperiod of time may evaporate the lymph from the tissue surface but maygenerate substantial damage. During the remaining 75% to 95% of a lowfrequency period, low intensity plasma jet (i.e., gray lines in FIG. 86“CH-1”) may be discharged. This low intensity plasma may have minimal orno effect on the tissue being treated. Accordingly, low intensity plasmaflow length may be minimized by increasing the frequency ofhigh-frequency pulses.

In some embodiments, a coagulation procedure may refer to controlledheating of the tissue to generate coagulation in a thin layer of tissueduring operation to prevent blood or lymph flow to the tissue surface.Coagulation may be a natural process during wound healing. Withcoagulation procedures, a similar effect may be achieved by controlledheating of the tissue. For coagulation, the previously discussedcontrolled heating procedures may adjusted to obtain the requiredeffect.

As previously mentioned, the absolute value of current may be notsignificant because the same current produces substantially differenteffects when applied to different handpieces. Rather, the ratio ofcurrent to the diameter of heating portion 124 (e.g., dheat) may have agreater significance. The base current-to-heating-portion-diameter ratiomay be referred to as I or “diameter current.” The power supply used forsuch flows may be able to generate (and transmit to the handpiece) ageneralized diameter current-time profile as shown in FIG. 87 that maybe used for a variety of medical applications. Referring to thediscussion above, this diameter current-time profile shows various basediameter currents. It should be understood that each of the basecurrents may have corresponding pulses.

In some embodiments, the diameter current may oscillate between lowdiameter current I_(L) and high diameter current I_(H). In someembodiments, low diameter current I_(L) may be in the range of betweenabout 5 A/mm and about 20 A/mm, and diameter current I_(H) may be in therange of between about 25 A/mm and about 80 A/mm.

In some embodiments, as shown in FIG. 87 , the relatively low and highdiameter currents may not be uniform and may exhibit predeterminedvariations. For a low diameter current, these variations may occur atabout 5 ms intervals although different intervals in the range ofbetween about 1 ms and about 10 ms are contemplated. In someembodiments, the low diameter current may correspond to up to 10variations per low frequency period, but in some embodiments, such asthe one shown in FIG. 24 , no low diameter current variations occur. Insome embodiments, the magnitude of low diameter current variations maybe in the range of between about 2 A/mm and about 5 A/mm, but departuresfrom this range are also contemplated. In some embodiments, for highdiameter current, these variations occur at about 1 ms intervals,although different intervals in the range of between about 0.2 ms andabout 2 ms may be also contemplated. In some embodiments, the highdiameter current may include up to about 5 variations per low frequencyperiod, but in some embodiments, such as the one shown in FIG. 24 , nohigh diameter current variations occur. The magnitude of high diametercurrent variations may be in the range of between about 5 A/mm and about10 A/mm.

In some embodiments, and as shown in FIG. 87 , the current-time profilemay be periodic with the period (t₁) in the range of between about 6 msand about 65 ms, although departures from this period may be alsocontemplated.

FIG. 88 shows a temperature-time profile that is associated with thecurrent-time profile depicted in FIG. 87 , with I1 corresponding to T1,I2 corresponding to T2, and so forth. The temperature-time profiledepicted in FIG. 88 can produce plasma flows CH-1 and CH-2 depicted inFIG. 86 . Specifically, in FIG. 88 , the high intensity plasma flow maybe produced by varying the high intensity base temperature according toa rectangular pulse train. In this example, the high intensity basetemperature may have two levels at T5 and T6 and follows the patternsshown in FIG. 88 (T6-T5-T6-T5-T6). In some embodiments, the highintensity base temperature lasts for time t2 and each period of constantbase temperature lasts for time Δt2. In some embodiments, high frequencypulses that have temperature T6 as the base may reach temperature T8 andhigh frequency pulses that have temperature T5 as a base may reachtemperature T7. In some embodiments, high-intensity high-frequencypulses may have a frequency f2 and the duty cycle D2. In someembodiments, the low intensity plasma flow may be produced by varyingthe low intensity base temperature according to a rectangular pulsetrain. In this example, the low intensity base temperature may have twolevels at T1 and T2 and follows the patterns (T1-T2-T1-T2-T1). In someembodiments, the low intensity base temperature may have a duration oftime t3 and each period of constant base temperature may have a durationof time Δt1. In some embodiments, high frequency pulses havingtemperature T1 as the base may reach temperature T3 and high frequencypulses that have temperature T2 as the base may reach temperature T4.The high frequency pulses have a frequency f1 and duty cycle D1. In someembodiments, the low frequency period for this temperature-time profilemay be t1. Table 7 sets forth example values for the above parameters.In some embodiments, variations from these example values may also beused to produce lymphosealing.

TABLE 7 Lymphosealing T1, K 3,000 t1, ms 30 T2, K 4,000 t2, ms 5 T3, K12,000 t3, ms 25 T4, K 13,000 Δt1, ms 5 T5, K 14,000 Δt2, ms 1 T6, K15,000 f1,kHZ 40-50 T7, K 16,000 D1 0.5 T8, K 17,000 f2, kHZ 25-30 D10.3-0.4

Adipose Tissue Dissection

Energy devices configured for adipose tissue dissection typicallygenerate large quantities of smoke. For example, electrosurgical, laser,and ultrasonic devices may deliver concentrated thermal energy tovaporize adipose (e.g., fat) tissue, which generates smoke. The devices,systems, and methods described herein may be configured to dissectadipose fat without generating smoke, for example, by precisely meltingadipose tissue into liquid, which can be removed, e.g., by mechanicalforce, before there is any vaporization. In some embodiments, a lowintensity plasma jet having a duration of between of about 5 ms andabout 10 ms may deliver energy sufficient to melt a surface of adiposetissue without melting underlying tissue. This can be followed bydelivery of a high intensity plasma jet with a high dynamic pressure butlow thermal energy for a duration of between about 0.5 ms and about 1 msto remove the melted adipose tissue.

Generally, adipose or fat tissue can melt at a temperature between about30° C. and about 50° C. In some embodiments, a melting heat may bebetween about 140 kJ/kg and about 200 kJ/kg. In some embodiments, avaporization temperature can be between about 200° C. and about 300° C.In some embodiments, the heat of vaporization can be between about 250kJ/kg and about 400 kJ/kg. Since these thermodynamic properties can beclose to each other, it can be important to precisely control energydelivery such that fat tissue is melted without vaporization (or withreduced vaporization).

In some embodiments, a target plasma temperature between about 2,000 Kand about 3,000 K, and an initiator plasma temperature between about8,000 K and about 10,000 K may allow control of thermal energy for a lowintensity plasma jet. In some embodiments, a pulse repetition period maybe between about 40 μs and about 50 μs with a duty D between about 0.3and about 0.4. In some embodiments, a radially oscillated plasma jet mayinclude a jet volume having a homogenous temperature distribution and alength of active jet. In some embodiments, a relatively short durationlow intensity plasma jet may be configured to heat an adipose tissuesurface below its vaporization point.

In some embodiments, a high intensity jet may include a target plasmatemperature between about 8,000 K and about 10,000 K, and an initiatorplasma temperature between about 14,000 K and about 16,000 K. A pulserepetition period may be between about 40 μs and about 50 μs and a dutyD may be between about 0.3 and about 0.4. These parameters ranges mayallow kinetic energy and a dynamic pressure jet to remove melted adiposetissue but prevent vaporization by having a short duration. The periodand duty for high frequency current pulses may be similar to the volumesof low and high intensity jets. A low frequency pulse duty D may bebetween about 5% and about 10% (e.g., about 0.05 and about 0.1) to avoidsurface heating and allow kinetic energy to remove melted adiposetissue. In some embodiments, a jet outlet diameter of about 0.5 mm withthe thermodynamic properties provided above may use an argon gas flowbetween about 0.15 L/min and about 0.2 L/min.

5. Embodiments for Generating Radially Expanded Plasma Flows

It will be appreciated that the present disclosure may include any oneand up to all of the following embodiments.

Embodiment 1—HF Pulses to Generate Predominate Radially Expanded PlasmaFlow

HF pulses to generate predominant radial expansion plasma flow maycomprise one or more of:

-   -   1. Base temperature level T_(BASE) being set by requirements of        the type of action. For example, base temperature level T_(BASE)        may be set to relatively low level such as about 2,000 K to        about 4,000 K for controlled heating of an object without        vaporization and sublimation of surface boundary and to a        relatively higher level of about 9,000K to about 11,000 K for        controlled speed of vaporization of surface boundary    -   2. Period of pulses repetition T being between about 10 μs and        about 50 μs    -   3. Temperature pulse rise and fall times τ₁ and τ₂ being        (0.01-0.1)·T. Temperature can vary (e.g., rise and fall) during        a pulse-interval oscillation.    -   4. Temperature pulse delay fall time τ₃ being (0.2-0.4)·T    -   5. Pulse temperature T_(PULSE) ^(t) (top optimal boundary of        T_(PULSE) for the given T_(BASE)) being:

$\frac{a\left( T_{base} \right)}{a\left( T_{pulse} \right)} = 0.5$

-   -   6. Pulse temperature T_(PULSE) ^(b) (bottom optimal boundary of        T_(PULSE) for the given T_(BASE)) being:

$\frac{a\left( T_{base} \right)}{a\left( T_{pulse} \right)} = 0.6$

-   -   7. Pulse temperature T_(FALL)=(0.2-0.4)(T_(PULSE)        ^(b)-T_(BASE)).

FIG. 89 depicts an example HF pulse with the associated temperatureparameters.

Embodiment 2—Method for Generating Predominantly Radially ExpandedPlasma Flow

A method to generate plasma flow with predominantly radially expandedplasma flow can involve one or more of the following considerations.

The outlet plasma flow with controlled degree of radial expansion isdefined by the following input parameters: the outlet temperature-timeprofile of plasma flow, where the structure of temperature-time profilemay define the shape of the plasma flow and average plasma particleenergy; the inlet gas flow, where the inlet gas flow affects the workingpressure in the active chamber of plasma-generating device and definesthe range of outlet energy flow; the outlet diameter ofplasma-generating device, where adaptive expansion nozzle increases theplasma flow velocity; the diameter or design of heating channel, whichmay affect the working pressure of plasma generating gas inside theactive chamber of plasma-generating device.

The controlled radial expansion of plasma flow may be obtained withplasma-generating device if the following criteria are met: the energyapplied to plasma-generating device may result in specific pattern ofoutlet temperature-time profile. The temperature-time profile mayinclude repeated changes/switches between base and pulse temperaturevalues, that correspond to base and pulse plasma flows, a density ratioof base to pulse plasma flow may be at least 2, a speed of sound of thepulse plasma flow at the pulse temperature may be at most 4 times thespeed of sound of the base plasma flow at the base temperature, and thefrequency of repetition may be higher than 1 kHz.

The relationship between the outlet temperature-time profile of plasmaflow, the inlet gas flow, the outlet diameter of plasma-generatingdevice, and diameter of heating channel meet the following requirementsto form the steady plasma flow and avoid turbulent mode: Outlet diametermay be less than certain value d_(OUT) ^(max), that is defined by outletpulse temperature. d_(OUT) ^(max) may be about 140 mm for pulsetemperature of 10,000 K; d_(OUT) ^(max) may be about 160 mm for pulsetemperature of 12,000 K; d_(OUT) ^(max) may be about 85 mm for pulsetemperature of 14,000 K; d_(OUT) ^(max) may be about 40 mm for pulsetemperature of 16,000 K; or d_(OUT) ^(max) may be about 30 mm for pulsetemperature of 24,000 K.

To avoid turbulent mode, the inlet gas flow rate may be less thancritical inlet gas flow for pulse and base plasma flows with a Reynoldsnumber of about 2,000. The maximum inlet gas flow rate G_(IN) may belinearly proportional to outlet diameter and defined by outlet pulse orbase temperature. The maximum inlet gas flow G_(IN) may be in a range ofbetween about 0.5l/min to about 4 l/min for an outlet diameterd_(OUT)=0.5 mm; the maximum inlet gas flow G_(IN) may be in a range ofbetween about 5 l/min to about 40 l/min for an outlet diameter d_(OUT)=5mm; or the maximum inlet gas flow G_(IN) may be in a range of betweenabout 10l/min to about 80l/min for an outlet diameter d_(OUT)=10 mm.

Mass flux in a heating channel may be sufficient to provide minimalworking pressure to maintain plasma flow. The minimum inlet gas flowrate G_(IN) may be linearly proportional to the square of a heatingchannel diameter and defined by outlet pulse and base temperature.

$\left( {G_{IN} > {{K \cdot \frac{\pi d_{H}^{2}}{4}}\left( {D + {\sqrt{\frac{T_{P}}{T_{B}}}\left( {1 - D} \right)}} \right)}} \right).$

In some embodiments, a minimum inlet gas flow G_(IN) may be about 0.03l/min to about 0.04 l/min for a heating channel diameter d_(H)=0.4 mm; aminimum inlet gas flow G_(IN) may be about 0.12l/min to about 0.15l/minfor a heating channel diameter d_(H)=0.8 mm; and/or a minimum inlet gasflow G_(IN) may be about 12 l/min to about 15 l/min for a heatingchannel diameter d_(H)=8 mm.

An outlet temperature-time profile for predominantly radially expandedplasma flow may comprise repeating five regions with the total durationof T of about 10 μs to about 50 μs. In a first region, the temperaturemay be maintained at the base temperature. Base temperature levelT_(BASE) may be based on a type of action. For example, T_(BASE) can beset to relatively low level (e.g., about 2,000 K to about 4,000 K) forcontrolled heating of an object without vaporization and sublimation oftreated surface boundary and to relatively higher level (e.g., about9,000 K to about 11,000 K) for controlled speed of vaporization ofsurface boundary. In a second region, the temperature may rapidly riseto a top pulse temperature during a time interval (0.01-0.1)T. In athird region, the temperature may be slightly reduced to a bottom pulsetemperature. In a fourth region, the temperature may be rapidly reducedto an intermediate value T_(FALL) during a time interval (0.01-0.1)T. Infifth region, the temperature may be reduced to an initial basetemperature during a time interval (0.2-0.4)T. A ratio of sound speed ofthe base plasma flow at the base temperature to sound speed of pulseplasma flow at a top pulse temperature may be equal to about 0.5.

$\left( {\frac{a\left( T_{base} \right)}{a\left( T_{t\_{pulse}} \right)} = 0.5} \right).$

A ratio of sound speed of the base plasma flow at the base temperatureto sound speed of pulse plasma flow at a bottom pulse temperature may beequal to about 0.6.

$\left( {\frac{a\left( T_{base} \right)}{a\left( T_{b\_{pulse}} \right)} = 0.6} \right).$

An intermediate temperature may be given byT_(FALL)=(0.2-0.4)·(T_(PULSE)-T_(BASE)).

An outlet temperature-time profile for predominantly radially expandedplasma flow may demonstrate optimal parameters for maximal radialexpansion of plasma flow. However, some applications might require afine adjustment of the degree of radial expansion and the shape ofplasma jet. The following examples demonstrates how the plasma jet shapecan be adjusted by varying the parameters: an increase of the totalduration T from about 25 μs to about 50 μs may result in elongation ofplasma jet shape; varying the optimal pulse temperature may result innon-equal volumes of base and pulse plasma flows and correspond toradially expanded plasma jet shape with small portion of laminar flow atthe end; increasing the duration ratio of pulse to base plasma flow mayresult in smaller degree of radial expansion; varying thetemperature-time profile shape may result in a different distribution ofdegree of radial expansion along the plasma jet axis; varying the inletgas flow, the diameter of heating channel, the outlet diameter mayaffect the size of plasma flow and correspond to different volume energydistribution of the plasma flow.

In some embodiments, there can be deviations from the outlettemperature-time profile described above. For example, some therapeuticapplications may use high temperature (e.g., greater than about 10,000°C.) pulse plasma flow and low temperature base plasma flow with low dutyto provide rapid cooling of the plasma flow. For instance, a duration ofpulses may be about 10 μs to about 25 μs, and the period T may be in arange of between about 50 μs to about 50 ms. Thus, the duty cycle may besubstantially lower than the optimum range. The remaining small fractionof radially expanded plasma flow may produce high concentration ofnitric oxide and due to low duty cycle of the pulses the resultingplasma flow may be effectively cooled down to desired temperature forsubsequent use.

The working pressure in the active chamber may play an important role tocontrol the outlet radially expanded plasma flow. Higher workingpressure may allow an adaptive nozzle design that leads to the increaseof the absolute velocity of outlet plasma particles, thus increasing thesize of radially expanded plasma jet. The increase of plasma jet sizewithout changing the temperature-time profile may spread the energy flowto higher area of treated surface that may be desirable for someprocedures. The working pressure may remain steady while the outlettemperature is oscillating between base and pulse value for the widerange of frequencies. The established value of working pressure may bedefined by an outlet temperature-time profile, the inlet gas flow andthe diameter/design of heating channel. For some applications, excessiveoutlet static pressure may be avoided and adaptive nozzle diameter maybe chosen to reduce the static pressure to ambient conditions.

Methods described herein can allow for dynamic control of a plasma jetshape. The dynamic control may be based on slow modulation totemperature-time profile such that the level of base and pulse plasmatemperature changes with time leads to a change of plasma jet shape andaverage particle energy. The outlet temperature-time profile may includehigh-frequency (e.g., greater than about 1 kHz) and low-frequency (e.g.,less than about 1 kHz) modulation of temperature. High-frequencymodulation may define the temporal plasma jet shape and may meet theabove written criteria to generate plasma jet with radial expansion.Low-frequency modulation may define the set of desired plasma jet shapesand duration of each of the shape. The modulation frequency may be lowerthan 1 kHz to avoid affecting the conditions for each plasma jet shape.

The low-frequency modulation may typically form at least two plasma jetshapes with two corresponding base temperatures. For example, plasmaflow with a lower base temperature may control the heating transferinside the treated specimen, and plasma flow with relatively high basetemperature may control the evaporation rate of the treated specimen.The structure of temperature-time profile with low and high frequencymodulations may be expressed in following way: the temperature changesbetween base and pulse level with frequency more than about 1 kHz; thebase level switches between at least two levels, such as low and highbase temperature; the frequency of these switches may be lower thanabout 1 KHz; the pulse level switches between low and high pulsetemperature and these switches may happen simultaneously andsynchronized with base level switches; for each pair of base and pulsetemperature levels the conditions for radial expansion of plasma jet maybe met; the duration of each base level switch may be defined by therequirement of a particular application; for some applications, thetemperature-time profile may also include the region with laminar plasmaflow. In this case, the temperature may stay at a base level for a fixedduration

The working pressure in the active chamber may remain steady even withadditional low-frequency modulation at least for the frequencies morethan about 10 Hz. This phenomenon may introduce additional ways toaffect the plasma jet shape. Low-frequency modulation oftemperature-time profile may be adjusted to tune the working pressure tothe desired level. For example, the increase of working pressure may bebeneficial to achieve bigger size of plasma flow shape with high basetemperature. The increase of the working pressure may be achieved byincreasing duration of plasma flow with high base temperature comparedto plasma flow with low base temperature. However, this may result inhigher energy impact of plasma shape with high base temperature that maynot be desirable. Alternatively, the working pressure may be increasedby applying a small oscillation of the low base temperature, whilemaintaining the plasma flow with high base temperature with the sameduration.

The method allows for independent control of the shape of plasma jet,the average temperature of plasma particles, and total energy fluxapplied to the treated specimen. The various shapes of plasma jet may beobtained by tuning the degree of radial expansion, that is defined byoutlet temperature-time profile. The average temperature of plasmaparticles may be controlled by shifting both base and pulse temperaturesto the desired level while the ratio between the base and pulsetemperatures may be adjusted to maintain the plasma jet shape. Theenergy flux may be adjusted by inlet gas flow and outlet diameter ofplasma-generating device.

In some embodiments, the method includes generation of radially expandedplasma flow with dynamic control over the plasma flow shape, and thepossibility of independent control of energy flux and average energy ofplasma particles for tuning the treatment procedure to achieve uniqueeffects by thermal interaction with the specimen. For example, thefollowing procedures may be achieved with this method:vaporization/sublimation of the object surface without heat transferinside the object; controlled heating of the material avoiding potentialdamage of the object due to local overheating; combined simultaneousvaporization/sublimation and controlled heating treatment with precisecontrol of vaporization rate and heat diffusion rate.

Embodiment 3—Arc Discharge Device for Generating Predominantly RadiallyExpanded Plasma Flows

An arc discharge plasma generating device can include an anode at adistal end of the device, the anode having a hole therethrough, aplurality of intermediate electrodes electrically insulated from eachother and from the anode, each of the intermediate electrodes having ahole therethrough, wherein the holes in the intermediate electrodes andthe hole in the anode form a hollow space having a first portion, whichover a substantial length of this portion has a uniform firstcross-sectional diameter, and a second portion, which over a substantiallength of this portion has a uniform second cross-sectional diameter,the second portion being closer to the anode than the first portion; acathode having a tapered distal portion narrowing toward a distal end ofthe cathode, a proximal end of the tapered portion being a base of thetapered portion, the tapered portion having a length being a distancefrom the base of the tapered portion to the distal end of the cathode;and an insulator sleeve extending along and surrounding only a portionof the cathode and having a distal end.

The following geometrical relationship between various parts of theplasma-generating device may be met: the ratio of the diameter ofcathode chamber (first cross-sectional diameter) and the diameter ofheating channel (second cross-sectional diameter) may be at least 4; adistance from the distal end of the cathode to the second portion of thehollow space (the heating channel inlet) may be at least 1.25 times thediameter of heating channel (second cross-sectional diameter); the gapbetween cathode and inner walls of insulator sleeve may be sufficient todeliver the required inlet gas flow without significant resistance inthe gap; the ratio of the length of the portion of cathode tipprotruding beyond the distal edge of insulator sleeve to the cathodediameter may be in the range of between about 1.0 to about 1.6; theprotruding portion may be selected to avoid the attachment of arc insidethe insulator sleeve; the ratio of the cathode tip length to cathodediameter may be in the range of between about 1.5 to about 2.0; thediameter of the heating portion may be in the range of between about 0.4to about 1.0 mm; the proposed diameter allows to achieve high outletplasma temperature of about 15,000 K to about 20,000 K; the biggerdiameter may be used in alternative embodiment if the high outlet plasmatemperature may not be required; the cathode diameter may be in range ofbetween about 0.5 mm to about 2 mm; the ratio of the length of the anodeportion to the diameter of the anode portion of the plasma channel maybe in the range of between about 2 to about 4. The proposed ratio may beoptimized to reduce heat losses to cooling system and provide properoperation for generating plasma flow. For surgical applications, theoutlet diameter of the anode portion may be in the range of betweenabout 0.3 mm to about 0.6 mm. For surgical applications, the outletdiameter of the anode portion may be in the range of between about 0.3to about 0.6 mm.

For surgical applications, the geometrical values of various parts ofthe plasma-generating device can include: heating channel diameter maybe about 0.4 mm; heating channel length may be about 1.2 mm; cathodediameter may be about 0.5mm; cathode tip length may be about 1.0 mm;cathode chamber diameter may be about_(1.8) mm; distance from the distalend of the cathode to the second portion of the hollow space (theheating channel inlet) may be about 0.7 mm; the length of the portion ofcathode tip protruding beyond the distal edge of insulator sleeve may beabout 1.4 mm; cathode chamber length may be about 2.1 mm; insidediameter of insulator sleeve may be about 1.2 mm; anode diameter may beabout 0.5 mm; anode length may be about 2 mm.

For therapeutic applications, the device can include: an anode havingadaptive nozzle with outlet anode diameter more than about 0.5 mm; alength of a heating channel may be about 3 mm to about 4 mm for gas flowof about 1.4 l/min. It is noted that the dimensions stated above merelyconstitute examples of the plasma-generating device and can be variedaccording to the field of application and the desired plasma properties.

An alternative example of plasma-generating device may comprise anisolator of complex shape that replaces the insulator sleeve, and aplurality of electrodes and separators between them. The shape of theisolator may copy the inner walls of insulator sleeve, cathode chamber,and heating portion described herein.

The arc discharge plasma generating device may be configured to suppressthe overheating of the cathode during operation with predominantlyradially expanded plasma flow. The expanded cathode chamber diameter maysuppress the overheating effects of the cathode during the operation.The smaller diameter of heating channel may allow high plasmatemperatures for operation with radially expanded plasma flow. Thelength of the heating channel and anode channel may be balanced tosufficiently heat the plasma-generating gas and avoid the high heatlosses to the cooling system. An anode may have an adaptive nozzle shapethat allows a boost to the absolute velocity of the outlet plasma flowthat may be beneficial to achieve higher size of plasma jet.

Embodiment 4—Generator for Plasma Generating Device to GeneratePredominantly Radially Expanded Plasma Flows

A current control generator may be configured to supply current to aplasma-generating device to generate radially expanded plasma flow withdynamic control of a plasma jet shape may include of one or moreprocessors that can meet the following current output requirements:provide low frequency current oscillation with current pulse resolutionin a range of between about 0.1 ms to about 0.2 ms; provide highfrequency current oscillation with current pulse resolution in a rangeof between about 0.1 μs to about 1 μs; provide synchronization of thehigh and low frequency current oscillation; the current controlgenerator may be configured to provide RMS current to cover a wholerange of desired plasma temperatures; the plasma temperature may beestimated as proportional to ratio of current to the diameter of heatingchannel; for a plasma-generating device with size constraints, such asfor keyhole surgeries, the max RMS current may be limited to about 12 Ato about 15 A to provide efficient cooling of the device duringoperation.

The high frequency current oscillation pattern for predominant radialexpansion of plasma flow may comprise repeating 5 regions, where thetotal duration may be T=10 μs to 50 μs. In a first region, the currentmaintained at the base current. Base current level I_(BASE) may bedefined by the required type of action. For example, a ratio of basecurrent to a heating channel diameter I_(BASE)/d_(H) may be set torelatively low level (e.g., about 7 A/mm to about 10 A/mm) forcontrolled heating of object without vaporization and sublimation oftreated surface boundary and to a relatively higher level of about 25A/mm to about 35 A/mm for controlled speed of vaporization of surfaceboundary. In a second region, the current rapidly rises to top pulsecurrent during time interval (0.01-0.1)·T. In a third region, thecurrent may be slightly reduced to bottom pulse current. In a fourthregion, the current may be rapidly reduced to intermediate valueI_(FALL) during time interval (0.01-0.1)T. In a fifth region, thecurrent may be reduced to initial base temperature during time interval(0.2-0.4)T. A ratio of sound speed of the base plasma flow at the basecurrent to sound speed of pulse plasma flow at top pulse current may beequal to about 0.5.

$\left( {\frac{a\left( I_{base} \right)}{a\left( I_{t\_{pulse}} \right)} = 0.5} \right).$

A ratio of sound speed of the base plasma flow at the base current tosound speed of pulse plasma flow at bottom pulse current may be equal toabout 0.6.

$\left( {\frac{a\left( I_{base} \right)}{a\left( I_{b\_{pulse}} \right)} = 0.6} \right).$

An intermediate current T_(FALL)=(0.2-0.4)·(I_(PULSE) ^(b)-I_(BASE)).

The high frequency current oscillation pattern may deviate from theseparameters if a desired degree of radial expansion is lower or thedesired shape of plasma flow may not be uniform. The following examplesdemonstrates how the plasma jet shape may be adjusted by varying thefollowing parameters: increase the total duration T from about 25 μs toabout 50 μs may result in elongation of plasma jet shape; varying thepulse current values may result in non-equal volumes of base and pulseplasma flows and correspond to radially expanded plasma jet shape with asmall portion of laminar flow at the end; increasing the duration ratioof pulse to base plasma flow may result in a smaller degree of radialexpansion; varying the current pattern shape may result in a differentdistribution of degree of radial expansion along the plasma jet axis;the low and high frequency current oscillation pattern may be definedbased on a type of procedure. Generalized low and high frequency currentpattern may be expressed in the following way: low-frequency modulationdefines the set of the desired plasma jet shapes and duration of each ofthe shape. The typical period of these modulations may be in the rangeof between about 0.5 ms and about 10 ms, that allow to avoid affectingthe conditions for each plasma jet shape to cover variations in thermalprocedures; high-frequency modulation defines the temporal plasma jetshape; the low-frequency modulation may typically form at least twoplasma jet shapes with two corresponding base currents. For example,plasma flow with lower base current may control the heating transferinside the treated specimen, and plasma flow with relatively high basecurrent may control the evaporation rate of the treated specimen.

A current pattern may have the following structure: the base currentswitches between at least two levels, such as low and high base current(I_(BL) and I_(BH)). The frequency of these switches may have a periodin a range of between about 0.5 ms and about 10 ms (or a frequencybetween about 100 Hz and about 2000 Hz). Each of these base currents maycorrespond to a plasma flow of low and high intensity of energy. Plasmaflow of low intensity may be used for controlled heat transfer insidethe treated specimen, and plasma flow of high intensity may be used forcontrolled vaporization/sublimation of the treated specimen. A durationratio of high to low base current (duty of low frequency currentmodulation) may be used for a precise tuning heat transfer andvaporization/sublimation rates. For each base current, there may be asynchronized high frequency current modulation. For maximum degree ofradial expansion, high frequency current modulation may follow the highfrequency current oscillation pattern for predominant radial expansion.For a specific shape of the plasma flow, the high frequency currentmodulation may deviate from the parameters as described above. Ifapplication requires laminar plasma flow for the particular base currenthigh frequency modulation may be suppressed to achieve constant basecurrent. Each high frequency modulation can be characterized by periodwhich may be in a range of between about 10 μs to about 50 μs and highfrequency duty.

The parameters for generating predominantly radially expanded flows canbe set according to predetermined ranges, as set forth in Table 6,described in the section above.

For some applications of current pattern, it can be desirable toincrease the working pressure inside the active chamber of aplasma-generating device and keep plasma flow of high intensity with thesame duration. This may be achieved by adding to low frequencymodulation a small oscillation of low base current. For example, the lowbase current may additionally oscillate with a period of about 0.5 ms toabout 1 ms. Alternatively, a number of base currents with variousduration may correspond with high frequency modulation for each basecurrent.

The current control generator may dynamically control a plasma jetshape. The dynamic control may comprise additional slow modulation to atemperature-time profile: the current control generator may beconfigured to operate for a set of procedures based on the method togenerate radially expanded plasma flow with dynamic control of plasmajet shape. The generalized current pattern may be adjusted to thedesired procedure by changing appropriate parameters, and allow for thegeneration of a dynamically controlled plasms flow with independentcontrol over the plasma flow shape and average energy of plasmaparticles. The freedom of controlling the key parameters allows todesign and tune the treatment procedure to achieve unique effects bythermal interaction with the specimen, that may not possible with anyother instruments. For example, the following procedures can be achievedwith the proposed embodiment of current pattern:vaporization/sublimation of the object surface without heat transferinside the object; controlled heating of the material avoiding potentialdamage of the object due to local overheating; combined simultaneousvaporization/sublimation and controlled heating treatment with precisecontrol of vaporization rate and heat diffusion rate; current patternadjustment to tune the procedure to more specific effect. Some examplesof such procedures for surgical applications may include lympho-sealing,tissue coagulation, tissue dissection, and tissue cutting.

Embodiment 5—System for Generating Predominantly Radially ExpandedPlasma Flows

A system for generating and discharging a plasma flow with dynamiccontrol of plasma jet shape may comprise: a plasma-generating deviceconfigured to generate a dynamically controlled plasma flow, and a gasflow controller configured to supply a plasma-generating gas to theplasma-generating device at a flow rate.

The inlet pressure may be maintained constant. This can be achieved bystoring sufficient amount of gas in the expansion chamber, so thepressure may not drop when the base plasma flow drains the considerableamount of gas. The volume of expansion chamber may be at leastV_(EXP)=N·G_(B)·T (1-D), where factor N—is number that needs to be equalto at least 2-5 to preserve the inlet pressure fluctuation.

A current control generator may be configured to supply a current to theplasma that meet the following criteria for current modulation: providelow frequency current oscillation with current pulse resolution in rangeof between about 0.1 ms to about 0.2 ms; provide high frequency currentoscillation with current pulse resolution in a range of between about0.1 μs to about 1 μs; provide synchronization of the high and lowfrequency current oscillation; provide RMS current that corresponds tomaximum RMS current that can be used in plasma-generating device.

Embodiment 6—Method of Generating Radially Expanded Plasma Flow

Embodiment 6: A method of generating radially expanded plasma flow maycomprise applying, to plasma-generating gas supplied to aplasma-generating device, energy that alternates between being at a baselevel for a first duration and at a pulse level for a second durationaccording to a controlled pattern; generating, in response to applyingthe energy, a plasma flow having a directional axis; discharging, fromthe outlet of the plasma-generating device, the plasma flow alternatingbetween a base configuration and a pulse configuration according to thecontrolled pattern, the plasma flow in the base configuration having (1)a first temperature at the outlet and (2) a first flow front thatadvances along the directional axis; the plasma flow in the pulseconfiguration having (1) a second temperature at the outlet that isgreater than the first temperature and (2) a second flow front thatadvances along the directional axis at a speed greater than the firstflow front such that a distance traversed by the second flow frontduring the second duration is substantially the same as a distancetraversed by the first flow front during the first duration and thesecond duration.

The method of Embodiment 6, wherein the plasma flow in the baseconfiguration includes plasma having a first density at the firsttemperature, and the plasma flow in the pulse configuration includesplasma having a second density at the second temperature, the firstdensity being at least twice the second density.

The method of Embodiment 6, wherein the plasma flow in the baseconfiguration includes plasma having a first speed of sound at the firsttemperature and the plasma flow in the pulse configuration includesplasma having a second speed of sound at the second temperature, thesecond speed of sound being at most four times the first speed of sound.

The method of Embodiment 6, wherein the first temperature is betweenabout 2,000 K and about 4,000 K.

The method of Embodiment 6, wherein the second temperature is less thanor equal to 15,000 K, a ratio of a flow rate G (L/min) of theplasma-generating gas to a diameter d (mm) of the outlet is less than orequal to 100, and a sum of the first and second durations is less than

$100,000*{\frac{d^{4}}{G^{2}}.}$

The method of Embodiment 6, wherein the second temperature is less thanor equal to 15,000 K, a ratio of a flow rate G (L/min) of theplasma-generating gas to a diameter d (mm) of the outlet is greater than100, and a sum of the first and second durations is less than 5 ms.

The method of Embodiment 6, wherein the second temperature is greaterthan 15,000 K, a ratio of a flow rate G (L/min) of the plasma-generatinggas to a diameter d (mm) of the outlet is less than or equal to 100, anda sum of the first and second durations is less than

$5,000*{\frac{d^{4}}{G^{2}}.}$

The method of Embodiment 6, wherein the second temperature is greaterthan 15,000 K, a ratio of a flow rate G (L/min) of the plasma-generatinggas to a diameter d (mm) of the outlet is greater than 100, and a sum ofthe first and second durations is less than 500 μs.

Embodiment 7—System for Generating Radially Expanded Plasma Flow

Embodiment 7: A system for generating radially expanded plasma flow maycomprise a current generator configured to generate a current having acontrolled pattern, the controlled pattern including: a first set ofoscillations between a first base level and a first pulse level, thefirst pulse level being higher than the first base level; and a secondset of oscillations between a second base level and a second pulselevel, the second pulse level being higher than the second base level;and a plasma-generating device configured to: heat, in response to thecurrent being applied to a heating portion of the plasma-generatingdevice, a plasma-generating gas to generate a plasma flow within theplasma-generating device; and discharge, from an outlet of theplasma-generating device, the plasma flow alternating between a firstconfiguration having a first degree of radial expansion and a secondconfiguration having a second degree of radial expansion, according tothe controlled pattern of the current.

The system of Embodiment 7, wherein second base level is greater thanthe first base level, and the second pulse level is greater than thefirst pulse level.

The system of Embodiment 7, wherein the heating portion includes aheating channel, and a diameter of the heating channel is no more thanabout 0.4 mm.

The system of Embodiment 7, wherein a diameter of the outlet is greaterthan a diameter of the heating channel.

The system of Embodiment 7, wherein the first degree of radial expansionis greater than the second degree of radial expansion.

The system of Embodiment 7, wherein the plasma flow includes an activezone defined by plasma having a temperature above 1,000 K, the activezone having a diameter that is at least ten times greater than adiameter of the outlet.

Embodiment 8—Plasma-Generating Device for Generating Radially ExpandedPlasma Flows

Embodiment 8: A plasma-generating device for generating radiallyexpanded plasma flow may comprise a cathode including a tapered distalportion; an anode disposed downstream from the cathode and beingelectrically insulated from the cathode, the anode defining an openingtherethrough; a plurality of intermediate electrodes disposed betweenthe cathode and the anode, the plurality of intermediate electrodeselectrically insulated from each other and from the anode and thecathode, each intermediate electrode from the plurality of intermediateelectrodes defining an opening therethrough such that the openings inthe plurality of intermediate electrodes and the anode collectivelydefine a plasma channel for discharging a plasma flow, the plasmachannel including: a first portion having a first cross-sectionaldiameter; and a second portion having a second cross-sectional diameter,the first cross-sectional diameter being at least four times the secondcross-sectional diameter; and an insulator sleeve extending along asurrounding a portion of the cathode.

The plasma-generating device of Embodiment 8, wherein a distance from adistal end of the cathode to the second portion of the plasma channel isat least 1.5 times the second cross-sectional diameter.

The plasma-generating device of Embodiment 8, wherein the opening in theanode has a cross-sectional diameter at a proximal end of the anode thatis less than a cross-sectional diameter at a distal end of the anode.

The plasma-generating device of Embodiment 8, further comprising anouter sleeve coupled to the anode; and a divider disposed between theouter sleeve and the plurality of intermediate electrodes, the dividerwith outside surfaces of the plurality of intermediate electrode, anoutside surface of the anode, and an inside surface of the outer sleevecollectively defining a cooling channel for cooling the plasma channel.

The plasma-generating device of Embodiment 8, wherein the cathode isdisposed in a cathode chamber having a diameter dcc, the diameter dccbeing at least four times the second cross-sectional diameter.

The plasma-generating device of Embodiment 8, wherein a distance betweena distal end of the insulator sleeve and a distal end of the cathode isat least a diameter of the cathode and less than 1.6 times the diameterof the cathode.

The plasma-generating device of Embodiment 8, wherein a length of theanode is between two times to eight times a diameter of the anode.

Embodiment 9—Method of Treatment

Embodiment 9: A method of treatment may comprise discharging, from anoutlet of a plasma-generating device, a plasma flow having a directionalaxis, the plasma flow alternating between: a first configurationincluding plasma having a first temperature higher than 1,000 K betweenfirst and second points along the directional axis, the first pointbeing closer to the outlet than the second point; and a secondconfiguration including plasma having a second temperature higher than1,000 K between third and fourth points along the directional axis, thethird point being closer to the outlet than the fourth point and thefourth point being closer to the outlet than the second point; anddirecting the plasma flow at a treatment surface disposed between thesecond point and the fourth point.

The method of Embodiment 9, wherein discharging the plasma flowalternating between the first and second configurations includesdischarging the plasma flow in the first configuration for a firstduration and discharging the plasma flow in the second configuration fora second duration, the first duration being greater than the secondduration.

The method of Embodiment 9, wherein the discharging the plasma flow inthe first configuration for the first duration causes evaporation ofliquid from the treatment surface and does not cause substantial damageto the treatment surface.

The method of Embodiment 9, wherein the first duration is about fivetimes the second duration.

The method of Embodiment 9, wherein the first temperature alternatesbetween first and second values, the first value being lower than thesecond value, and the second temperature alternates between third andfourth values, the third value being lower than the fourth value andhigher than the second value.

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto; inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

As used herein, the terms “about” and/or “approximately” when used inconjunction with numerical values and/or ranges generally refer to thosenumerical values and/or ranges near to a recited numerical value and/orrange. In some instances, the terms “about” and “approximately” may meanwithin ±10% of the recited value. For example, in some instances, “about100 [units]” may mean within ±10% of 100 (e.g., from 90 to 110). Theterms “about” and “approximately” may be used interchangeably.

The specific examples and descriptions herein are exemplary in natureand embodiments may be developed by those skilled in the art based onthe material taught herein without departing from the scope of thepresent invention.

Unless otherwise specified, the illustrated embodiments can beunderstood as providing exemplary features of varying detail of certainembodiments, and therefore, unless otherwise specified, features,components, modules, and/or aspects of the illustrations can beotherwise combined, separated, interchanged, and/or rearranged withoutdeparting from the disclosed systems or methods. Additionally, theshapes and sizes of components are also exemplary and unless otherwisespecified, can be altered without affecting the scope of the disclosedand exemplary systems, apparatuses, or methods of the presentdisclosure.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

1. A method, comprising: supplying a plasma-generating gas to a plasmagenerating device having an outlet; applying energy to theplasma-generating gas according to a predetermined energy pattern; anddischarging, in response to applying the energy, a plasma flow from theoutlet of the plasma generating device, the plasma flow having aperiodic pattern including a base plasma flow and a pulse plasma flow,the base plasma flow having a first temperature at the outlet of thedevice, and the pulse plasma flow having a second temperature at theoutlet of the device that is greater than the first temperature, thebase plasma flow having a first density at the first temperature, andthe pulse plasma flow having a second density at the second temperature,the first density being at least two times the second density, the baseplasma flow having a first speed of sound, and the pulse plasma flowhaving a second speed of sound that is at most about four times greaterthan the first speed of sound.
 2. The method of claim 1, wherein thepattern includes alternating between discharging the base plasma flowfor a base duration and discharging the pulse plasma flow for a pulseduration, the pulse duration being less than the base duration.
 3. Themethod of claim 2, wherein the plasma-generating gas is supplied at apredetermined flow rate, and the sum of the base duration and the pulseduration is based at least in part on the flow rate.
 4. The method ofclaim 3, wherein the sum of the base duration and the pulse duration isfurther based on the second temperature.
 5. The method of claim 4,wherein: the second temperature is less than or equal to 15,000 K, aratio of the predetermined flow rate G of the plasma-generating gas to adiameter d of the outlet is less than or equal to 100, and the sum ofthe base duration and the pulse duration is less than$100,000*{\frac{d^{4}}{G^{2}}.}$
 6. The method of claim 4, wherein: thesecond temperature is less than or equal to 15,000 K, a ratio of thepredetermined flow rate G of the plasma-generating gas to a diameter dof the outlet is greater than 100, and the sum of the base duration andthe pulse duration is less than 5 ms. 7-8. (canceled)
 9. The method ofclaim 2, wherein a frequency of the alternating between the base plasmaflow and the pulse plasma flow is greater than about 1 kHz.
 10. Themethod of claim 1, wherein a diameter of the outlet is less than about140 mm when the second temperature is less than or equal to about 10,000K. 11-19. (canceled)
 20. The method of claim 1, wherein the firsttemperature is between about 2,000 K and about 4,000 K, and the secondtemperature is between about 7,500 K and about 26,500 K.
 21. A system,comprising: a current control generator configured to supply currenthaving a current pattern to a plasma-generating device such that theplasma-generating device can generate a radially expanded plasma flow,the current pattern including: a first set of oscillations between afirst base level and a second base level, the second base level beinggreater than the first base level, the first set of oscillations havinga first frequency; and a second set of oscillations between a firstpulse level and a second pulse level, the second pulse level beinggreater than the first pulse level and the first and second base levels,the second set of oscillations having a second frequency greater thanthe first frequency, the first and second sets of oscillations beingsynchronized such that the first base level is paired with the firstpulse level for generating the radially expanded plasma flow and thesecond base level is paired with the second pulse level for generatingthe radially expanded plasma flow.
 22. The system of claim 21, whereinthe first set of oscillations have a current pulse resolution betweenabout 0.1 ms to about 0.2 ms.
 23. The system of claim 21, wherein thesecond set of oscillations have a current pulse resolution between about0.1 μs and 1 μs.
 24. The system of claim 21, wherein a root mean squareof the current having the current pattern is between about 12 A andabout 15 A. 25-31. (canceled)
 32. The system of claim 21, wherein thefirst frequency of the first set of oscillations is between about 100 Hzand about 2000 Hz.
 33. The system of claim 21, further comprising theplasma-generating device, the plasma-generating device configured to:heat, in response to receiving the current, a plasma-generating gas; anddischarge, in response to heating the plasma-generating gas, theradially expanded plasma flow alternating between a low intensity plasmaflow and a high intensity plasma flow from an outlet, the low intensityplasma flow being associated with the first base level and the highintensity plasma flow being associated with the second base level. 34.The system of claim 33, wherein the plasma-generating device isconfigured to discharge the low intensity plasma flow to heat a treatedspecimen.
 35. The system of claim 33, wherein the plasma-generatingdevice is configured to discharge the high intensity plasma flow tovaporize or sublimate a treated specimen.
 36. The system of claim 33,wherein the low intensity plasma flow has a first degree of radialexpansion, and the high intensity plasma flow has a second degree ofradial expansion that is different than the first degree of radialexpansion.
 37. (canceled)
 38. The system of claim 33, wherein the plasmaflow includes an active zone defined by plasma having a temperatureabove 1,000 K, the active zone having a diameter that is at least tentimes greater than a diameter of the outlet.
 39. A plasma-generatingdevice, comprising: a cathode including a tapered distal portion; ananode disposed downstream from the cathode and being electricallyinsulated from the cathode, the anode defining an opening therethrough;a plurality of intermediate electrodes disposed between the cathode andthe anode, the plurality of intermediate electrodes electricallyinsulated from each other and from the anode and the cathode, eachintermediate electrode from the plurality of intermediate electrodesdefining an opening therethrough such that the openings in the pluralityof intermediate electrodes and the anode collectively define a plasmachannel for discharging a plasma flow, the plasma channel including: afirst portion having a first cross-sectional diameter; and a secondportion having a second cross-sectional diameter, the firstcross-sectional diameter being at least four times the secondcross-sectional diameter; and an insulator sleeve extending along asurrounding a portion of the cathode.
 40. The plasma-generating deviceof claim 39, wherein a distance from a distal end of the cathode to thesecond portion of the plasma channel is at least 1.25 times the secondcross-sectional diameter.
 41. The plasma-generating device of claim 39,wherein a ratio of a length of a portion of the cathode protrudingbeyond a distal edge of the insulator sleeve to a maximum diameter ofthe catheter being between about 1.0 and about 1.6.
 42. Theplasma-generating device of claim 39, wherein a ratio of a length of thetapered distal portion of the cathode to a maximum diameter of thecathode is between about 1.5 and about 2.0.
 43. (canceled)
 44. Theplasma-generating device of claim 39, wherein the anode forms an anodeportion of the plasma channel, and a ratio of a length of the anodeportion to a diameter of the anode portion is between about 2 and about4. 45-46. (canceled)
 47. The plasma-generating device of claim 39,further comprising: an outer sleeve coupled to the anode; and a dividerdisposed between the outer sleeve and the plurality of intermediateelectrodes, the divider with outside surfaces of the plurality ofintermediate electrode, an outside surface of the anode, and an insidesurface of the outer sleeve collectively defining a cooling channel forcooling the plasma channel.
 48. The plasma-generating device of claim39, wherein the cathode is disposed in a cathode chamber having adiameter d_(CC), the diameter d_(CC) being at least four times thesecond cross-sectional diameter. 49-50. (canceled)
 51. The method ofclaim 1, further comprising lymphosealing a tissue using the plasma flowto reduce fluid discharge.
 52. The method of claim 1, further comprisingcoagulating a tissue using the plasma flow to reduce fluid flow.
 53. Themethod of claim 1, further comprising cutting or dissecting a tissueusing the plasma flow.
 54. The method of claim 1, further comprisingvaporizing or subliming a tissue without heat transfer inside the tissueusing the plasma flow.